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Big Ideas Math: Modeling Real Life, Grade 6

BI

Big Ideas Math: Modeling Real Life, Grade 6 View details

1. Multiplying Fractions

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Exercise 55 Page 51

Practice makes perfect

We want to find the area of our banner for the football rally. Notice that the banner is in the shape of a rectangle.

The formula for the area of a rectangle is the product of the length and the width of the figure. Area = l * w The length of the banner is 1 12 feet and the width is 4 23 feet. To multiply these numbers, we will first rewrite the expression so that all of its terms are fractions.

1 12 * 4 23

a bc=a* c+b/c

1* 2 +1/2 * 4* 3+2/3

Multiply

2 +1/2 * 12+2/3

Add terms

3/2 * 14/3

When multiplying fractions, remember that the product of two fractions is equal to the product of the numerators divided by the product of the denominators. Let's find the given product!

3/2 * 14/3

Multiply fractions

3* 14/2* 3

Multiply

42/6

Calculate quotient

7

So, the area of the banner is 7 square feet.

Now we want to add a 14-foot border on each side of the banner from Part A. Let's do it!

Let's rewrite this expression so that all of its terms are fractions.

(1 12+2* 1/4) * (4 23+2* 1/4)

MoveLeftFacToNum

a*b/c= a* b/c

(1 12+2* 1/4) * (4 23+2* 1/4)

a bc=a* c+b/c

(1* 2+1/2+2* 1/4) * (4* 3+2/3+2* 1/4)

Multiply

(2+1/2+2/4) * (12+2/3+2/4)

Add terms

(3/2+2/4) * (14/3+2/4)

a/b=.a /2./.b /2.

(3/2+2÷ 2/4÷ 2) * (14/3+2÷ 2/4÷ 2)

Calculate quotient

(3/2+1/2) * (14/3+1/2)

▼

Add fractions

a/b=a * 3/b * 3

(3/2+1/2) * (14/3+1* 3/2* 3)

a/b=a * 2/b * 2

(3/2+1/2) * (14* 2/3* 2+1* 3/2* 3)

Multiply

(3/2+1/2) * (28/6+3/6)

Add fractions

3+1/2 * 28+3/6

Add terms

4/2 * 31/6

The product of two fractions is equal to the product of the numerators divided by the product of the denominators. Let's find the given product!

4/2 * 31/6

Multiply fractions

4* 31/2* 6

Multiply

124/12

a/b=.a /4./.b /4.

124÷ 4/12÷ 4

Calculate quotient

31/3

▼

Write fraction as a mixed number

Rewrite 31 as 30+1

30+1/3

Write as a sum of fractions

30/3+1/3

Calculate quotient

10+1/3

Rewrite 10+1/3 as 10 13

10 13

As we can see, the area of the banner with the border is 10 13 square feet.

Subchapter links

Try It p.46-48

Self-Assessment for Concepts & Skills p.48

Self-Assessment for Problem Solving p.49

Review & Refresh p.50

Concepts, Skills, & Problem Solving p.50-52