2 Fractions 2.1 Fractions and Mixed Numbers Banking 1/3/2019 2 Fractions 2.1 Fractions and Mixed Numbers 2.2 Add and Subtract Fractions and Mixed Numbers 2.3 Multiply and Divide Fractions and Mixed Numbers Chapter 1

2.1 Fractions and Mixed Numbers Banking 1/3/2019 2.1 Fractions and Mixed Numbers OBJECTIVES Identify terms used with fractions. Distinguish between fractions and mixed numbers. Convert improper fractions to whole numbers. Convert improper fractions to mixed numbers. Chapter 1

2.1 Fractions and Mixed Numbers Banking 1/3/2019 2.1 Fractions and Mixed Numbers OBJECTIVES Convert mixed numbers to improper fractions. Reduce fractions to lowest terms. Raise fractions to higher terms. Convert fractions to decimals. Convert decimals to fractions. Chapter 1

Key Terms fraction numerator denominator proper fraction Banking 1/3/2019 Key Terms fraction numerator denominator proper fraction improper fraction mixed number lowest terms greatest common divisor equivalent fraction repeating decimal Chapter 1

Convert to a whole number. STEPS Divide 180 by 30. Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 3 Convert improper fractions to whole numbers. Example Convert to a whole number. STEPS Divide 180 by 30. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 4 Convert improper fractions to mixed numbers. Example Convert to a mixed number. STEPS Divide the numerator by the denominator. Place the remainder over the divisor. Write the mixed number as . Chapter 1

Convert to a mixed number. STEPS Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 4 Convert improper fractions to mixed numbers. Example Convert to a mixed number. STEPS Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 5 Convert mixed numbers to improper fractions. Example Convert to an improper fraction. STEPS Multiply the denominator by the whole number. 4 × 9 = 36 Add the product and the numerator. 36 + 1 = 37 Place the sum over the original denominator. Chapter 1

Convert the mixed number to an improper fraction. STEPS Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 5 Convert mixed numbers to improper fractions. Example Convert the mixed number to an improper fraction. STEPS Chapter 1

Convert the mixed number to an improper fraction. STEPS Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 5 Convert mixed numbers to improper fractions. Example Convert the mixed number to an improper fraction. STEPS Chapter 1

Reduce to lowest terms. STEPS Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 6 Reduce fractions to lowest terms. Example Reduce to lowest terms. STEPS Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 6 Reduce fractions to lowest terms. Example Write the fraction in lowest terms. STEPS Both 135 and 275 can be divided by 5. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 6 Reduce fractions to lowest terms. Example Write the fraction in lowest terms. STEPS Divide both 80 and 270 by 10. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 6 Reduce fractions to lowest terms. Example Reduce to lowest terms using the greatest-common-divisor method. STEPS Divide the denominator by the numerator. Divide the original divisor by the remainder. Continue dividing until there is no remainder. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 6 Reduce fractions to lowest terms. Example Reduce to lowest terms using the greatest-common-divisor method. STEPS The last divisor, 4, is the greatest common divisor and is used to divide 268 and 460. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 6 Reduce fractions to lowest terms. Example Show that the fraction is in lowest terms. STEPS The last divisor, 1, is the greatest common divisor. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 7 Raise fractions to higher terms. Example Raise to a fraction with a denominator of 12. STEPS Divide the new denominator by the original denominator. 12 ÷ 3 = 4 Multiply both the numerator and denominator by the quotient. 2 × 4 = 8 and 3 × 4 = 12 Write the new numerator over the desired denominator. Chapter 1

Write the fraction as a fraction with denominator 45. STEPS Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 7 Raise fractions to higher terms. Example Write the fraction as a fraction with denominator 45. STEPS Chapter 1

Write the fraction as a fraction with denominator 72. STEPS Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 7 Raise fractions to higher terms. Example Write the fraction as a fraction with denominator 72. STEPS Chapter 1

Convert the fraction to a decimal. STEPS Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 8 Convert fractions to decimals. Example Convert the fraction to a decimal. STEPS Chapter 1

Convert the fraction to a decimal. STEPS Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 8 Convert fractions to decimals. Example Convert the fraction to a decimal. STEPS Chapter 1

Below is a chart of decimal equivalents. Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 8 Convert fractions to decimals. Example Below is a chart of decimal equivalents. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 8 Convert fractions to decimals. Example Convert to a decimal. STEPS Convert the fractional part by dividing the numerator by the denominator. Write the whole number 5 with the decimal equivalent 0.625. 5.625 Chapter 1

Convert to a decimal. STEPS Divide 1 by 6. Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 8 Convert fractions to decimals. Example Convert to a decimal. STEPS Divide 1 by 6. Chapter 1

Convert to a decimal. STEPS Divide 1 by 3. Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 8 Convert fractions to decimals. Example Convert to a decimal. STEPS Divide 1 by 3. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 8 Convert fractions to decimals. Example Convert to a decimal. STEPS Convert the fractional part by dividing the numerator by the denominator. Write the whole number 8 with the decimal equivalent 0.42. 8.42 Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 9 Convert decimals to fractions. Example Convert 1.35 to a fraction. STEPS Write the decimal in its fractional form. Reduce to lowest terms. The fractional equivalent to 1.35 is . Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 9 Convert decimals to fractions. Example Convert 0.45 to a fraction. STEPS Write the decimal in its fractional form. Reduce to lowest terms. The fractional equivalent to 0.45 is . Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 9 Convert decimals to fractions. Example Convert 0.105 to a fraction. STEPS Write the decimal in its fractional form. Reduce to lowest terms. The fractional equivalent to 0.105 is . Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 9 Convert decimals to fractions. Example Convert 2.583 to a fraction. STEPS Write the decimal in its fractional form. The fractional equivalent to 0.105 is . Chapter 1

2.2 Add/Subtract Fractions and Mixed Numbers Banking 1/3/2019 2.2 Add/Subtract Fractions and Mixed Numbers OBJECTIVES Identify terms used with adding and subtracting fractions. Add and subtract like fractions. Find the least common denominator. Add and subtract unlike fractions. Add mixed numbers. Subtract mixed numbers. Chapter 1

Key Terms like fractions unlike fractions common denominator Banking 1/3/2019 Key Terms like fractions unlike fractions common denominator least common denominator (LCD) inspection method price number method prime number prime factorization Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 2 Add and subtract like fractions. Example Add. STEPS Add the numerators. 5 + 2 = 7 Write the result over the common denominator. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 2 Add and subtract like fractions. Example Subtract. STEPS Subtract the numerators. 11 – 7 = 4 Write the result over the common denominator. Reduce. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 2 Add and subtract like fractions. Example Add. STEPS Add the fractions. Convert the sum to a mixed number and then a decimal. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 2 Add and subtract like fractions. Example Add. STEPS Add the fractions. Convert the sum to a mixed number and then a decimal. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 3 Find the least common denominator. Example Find the least common denominator. STEPS By simple observation, the smallest common number that all the unlike denominators 2, 4, and 3 will evenly divide is 12. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 3 Find the least common denominator. Example Find the least common denominator. STEPS By simple observation, the least common number is 12 because 12 is the smallest number the denominators 4, 3, and 12 will evenly divide. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 3 Find the least common denominator. Example Find the least common denominator of and . STEPS Divide each denominator by a prime number common to two or more of the numbers. Write the quotient above each denominator. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 3 Find the least common denominator. Example Find the least common denominator of and . STEPS Each of the new quotients, 4, 6, and 10, can still be divided by 2. Therefore, continue the division process using the same prime number, 2. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 3 Find the least common denominator. Example Find the least common denominator of and . STEPS Continue to divide by the prime number 2. The new quotient 2 can still be divided by the prime number 2, but the quotients 3 and 5 cannot be evenly divided by 2. Because 3 and 5 cannot be evenly divided by 2, write these amounts in the row of answers. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 3 Find the least common denominator. Example Find the least common denominator of and . STEPS Because the prime number 2 will not evenly divide these last two quotients in the row, try the next prime number, which is 3. Because 1 and 5 are not divisible by 3, write these amounts in the row of answers. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 3 Find the least common denominator. Example Find the least common denominator of and . STEPS Because the prime number 3 will not evenly divide these last quotients, try the next prime number, 5. The last quotient can be divided by 5. Divide until all quotients are 1. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 3 Find the least common denominator. Example Find the least common denominator of and . STEPS Because no prime number can evenly divide these last quotients, determine the least common denominator by multiplying the five divisors. 2 × 2 × 2 × 3 × 5 = 120 120 is the least common denominator. Chapter 1

Add. STEPS Example Objective 2 Write a percent as a decimal. Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 4 Add and subtract unlike fractions. Example Add. STEPS Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 4 Add and subtract unlike fractions. Example Add and subtract. STEPS Find the least common denominator for 18, 20, and 24. 2 × 2 × 2 × 3 × 3 × 5 = 360 Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 4 Add and subtract unlike fractions. Example Add and subtract. STEPS Raise each fraction to 360ths, and then add or subtract. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 5 Add mixed numbers. Example Suppose you are a sales clerk in a fabric store who cut two pieces of trimming for a customer. One piece measured inches, and the other measured inches. Add the two pieces together to get the total measurement for the order. STEPS Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 5 Add mixed numbers. Example Add. STEPS Add the fractional parts and convert the improper fraction to a mixed number. Reduce to lowest terms, if necessary. Add the whole numbers. 11 + 3 = 14 Add the mixed number and the sum of the whole numbers. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 5 Add mixed numbers. Example Add. STEPS Determine the least common denominator. 10 Add the fractional parts. Add the whole numbers. 13 + 2 = 15 Add the whole numbers and the fractional parts. Chapter 1

Subtract. STEPS Example Objective 2 Write a percent as a decimal. Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 6 Subtract mixed numbers. Example Subtract. STEPS Chapter 1

Subtract. STEPS Example Objective 2 Write a percent as a decimal. Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 6 Subtract mixed numbers. Example Subtract. STEPS Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 6 Subtract mixed numbers. Example Subtract using borrowing. STEPS To subtract from the whole number 9, borrow or subtract 1 from the 9, the whole number in the minuend, and express it in sixths, as in . The 9 reduced by 1 is 8 because you borrowed 1 from it. Place the 8 beside the . Then subtract the fractions. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 6 Subtract mixed numbers. Example Subtract using borrowing. STEPS Determine a common denominator and change the fractions to equivalent fractions. Subtract the fractional parts and the whole numbers. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 6 Subtract mixed numbers. Example Subtract using borrowing. STEPS Borrow 1 from 3, leaving . Then subtract from . Chapter 1

2.3 Multiply/Divide Fractions and Mixed Numbers Banking 1/3/2019 2.3 Multiply/Divide Fractions and Mixed Numbers OBJECTIVES Multiply fractions. Use cancellation. Multiply whole numbers, fractions, and mixed numbers. Divide fractions. Divide whole numbers, fractions, and mixed numbers. Chapter 1

Banking 1/3/2019 Key Terms cancellation Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 1 Multiply fractions. Example Multiply. STEPS Multiply the numerators of the fractions. 5 × 3 × 1 = 15 Multiply the denominators of the fractions. 8 × 5 × 3 = 120 Rewrite the fraction and reduce. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 2 Use cancellation. Example Multiply. STEPS Determine the common factor that will evenly divide any one of the numerators and any one of the denominators. Cancel the numerator and denominator. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 2 Use cancellation. Example Multiply. STEPS Cancel. Multiply the numerators and denominators. 1 × 1 × 1 = 1 1 × 3 × 4 = 12 Write the fraction. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 3 Multiply whole numbers, fractions, and mixed numbers. Example Multiply. STEPS Convert to improper fractions and cancel. Multiply the numerators and denominators. Convert to a mixed number and reduce. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 3 Multiply whole numbers, fractions, and mixed numbers. Example Phillip Fontano earns $2,345 a month. He spends one-fifth of his monthly salary for rent. How much does he pay each month for rent. STEPS When a problem uses the word of, as in “He spends one-fifth of his monthly salary,” the word of means to multiply. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 3 Multiply whole numbers, fractions, and mixed numbers. Example Multiply. STEPS Convert the mixed numbers to improper fractions. Rewrite the problem and cancel if possible. Multiply. Convert the improper fraction to a mixed number. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 3 Multiply whole numbers, fractions, and mixed numbers. Example Multiply. STEPS Convert whole and mixed numbers to improper fractions. Rewrite the problem and cancel if possible. Multiply. Convert the improper fraction to a mixed number. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 4 Divide fractions. Example Divide. STEPS Invert the divisor and multiply. Convert the improper fraction to a mixed number and reduce. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 5 Divide whole numbers, fractions, and mixed numbers. Example Divide. STEPS Write the whole number as a fraction and invert the divisor. Cancel, if necessary, and multiply. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 5 Divide whole numbers, fractions, and mixed numbers. Example Divide. STEPS Convert each mixed number to an improper fraction. Invert the divisor, cancel, if necessary, and multiply. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 5 Divide whole numbers, fractions, and mixed numbers. Example Divide. STEPS Convert whole and mixed numbers to improper fractions. Invert the divisor and multiply. Convert improper fraction to a mixed number and reduce. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 5 Divide whole numbers, fractions, and mixed numbers. Example Divide. STEPS Convert whole and mixed numbers to improper fractions. Invert the divisor, multiply, and reduce, if necessary. Chapter 1

Banking 1/3/2019 Objective 2 Write a percent as a decimal. Objective 5 Divide whole numbers, fractions, and mixed numbers. Example A clothing shop makes vests that use yards of material. Find the number of vests that can be cut from a piece of linen fabric that is 8 yards in length. STEPS Chapter 1