35 Adding Fractions Add Estimate the sum x = = Find the least common denominator ~...(find the LCM of 8 and 5).. ~ 8: 8, 16, 24, 32, 40 ~ 5: 5, 10, 15, 20, 25, 30, 35, 40 ~ The LCM is 40. Change both denominators to 40...then change both numerators Add the new numerators, then keep the denominator the same. mixed number Convert to a mixed number. Is the sum close to the estimate? 40

Adding Fractions

18 Adding Mixed Numbers Add Estimate the sum x = = Find the least common denominator ~...(find the LCM of 10 and 4).. ~ 10: 10, 20, 30, 40 ~ 4: 4, 8, 12, 16, ~ The LCM is 20. Change both denominators to 20...then change both numerators Add the new numerators, then keep the denominator the same. mixed number Convert to a mixed number. Is the sum close to the estimate? Add the whole numbers to the sum

39 Subtracting Fractions Subtract Estimate the difference x = Find the least common denominator ~...(find the LCM of 14 and 6) ~ 14: 14, 28, 42, 56, 70, ~ 6: 6, 12, 18, 24, 30, 36, ~ The LCM is 42. Change both denominators to 42...then change both numerators Subtract the new numerators, then keep the denominator the same. Simplify by finding the GCF ~ 4: 1, 2, 4 ~ 42: 1, 2,... Is the sum close to the estimate? – 5656 – ÷ = 2 2 –

Subtracting Fractions

Rewrite each mixed number by borrowing Take one from 4 (now you have 3...)...then add it back to the fraction \ = Remember: 1 = 9999 Subtracting Mixed Numbers = = = =

16 Subtracting Mixed Numbers Estimate the difference x = Find the least common denominator ~...(find the LCM of 3 and 8).. ~ 3: 3, 6, 9, 12, 15, 18, 21, 24 ~ 8: 8, 16, 24 ~ The LCM is 24. Change both denominators to 24...then change both numerators Subtract the new numerators, then keep the denominator the same – To avoid negative fraction, let’s borrow from the whole number Take one from 7 (now you have 6...)...then add it back to the fraction \ = – Is the estimate close to the difference?

Adding Mixed Numbers Subtracting Mixed Numbers

Estimate the product.  4 9 = 36 Convert each to a simple fraction = \ \ = 40 Cross-simplify. Multiply numerators, then denominators Simplify the product. Multiplying Fraction and Mixed Numbers

Multiplying Fraction and Mixed Numbers

Dividing Fractions and Mixed Numbers Original number FractionReciprocal = = 6. 1 = =

3 8 5 ÷ 9 Estimate the quotient.  5 ÷ 9  1212 Convert each to a simple fraction 5 1 ÷ 75 8 = \ \ Cross-simplify. Multiply numerators, then denominators Dividing Fractions and Mixed Numbers Keep the first fraction the same Change the division to multiplication Flip the 2 nd fraction

Dividing Fractions and Mixed Numbers