GETTING THE IDEA To multiply fractions, multiply the numerators and multiply the denominators. Then simplify the resulting product if possible. When multiplying mixed numbers, first write them as fractions. The model shows how to find x. Draw an array with 8 equal parts. Shade of the array to represent the first factor. Then shade to represent the second factor. The overlapping shaded region shows that x =
EXAMPLE 1 Multiply x Step 1 Multiply the numerators x = 2 x 5 Step 2 Multiply the denominators x = 2 x 5 5 x 8 Step 3 Simplify / Solution =
EXAMPLE 2 Multiply x Strategy: Use rule for multiplying fractions. Step 1 Write the mixed number as a fraction x = x Step 2 Multiply the numerators and denominators. Divide the numerator and denominator by the common factor 7. x = 8 x 7 21 x 3 Step 3 Simplify and reduce. (solution) x =
FRACTIONS / DECIMALS Some situations require multiplying fractions with decimals. To do this, write the decimal as a fraction or write the fraction as a decimal. Then multiply. To multiply decimals, multiply as with whole number. Add the number of decimal places in each factor to find the number of decimal places in the product.
EXAMPLE 3 Ernesto bough ¾ pound of mixed nuts. How much did he spend? Mixed Nuts: $4.80 / lb Strategy: Write the fraction as a decimal and multiply. Step 1 Set up the problem ¾ x 4.80 Multiply the number of pounds by the price per pound. Step 2 Write the fraction as a decimal Divide 3 by 4 = 0.75 Step 3 Multiply the decimals 4.80 x0.75 2400 +3360 3.6000 Solution Ernesto spent $3.60 in all.
DIVIDING FRACTIONS To divide by a fraction, multiply by the reciprocal of the fraction. Keep, change, flip.
EXAMPLE 6 Jessie and Nicole’s lunch bill came to $11.26. They will split the bill evenly. How much is each person’s share of the bill? Strategy Divide the total cost by 2 Step 1 Set up the problem 2)11.26 Divide the cost of the lunch by 2 to find each person’s share. Step 2 Divide as with whole numbers and position the decimal point. 5.63 2)11.26move the decimal point from the dividend directly up Solution Each person’s share of the bill is $5.63.