44 Chapter 2 Multiplying and Dividing Fractions How can you use estimation to check that your answer is reasonable? STATE STANDARDS MA.6.A.5.3 S Fractions and Estimation 2.1 Work with a partner. Use the model for the whole to draw a model for the given fractions. ACTIVITY: Using Models for Fractions 1 1 Whole Model for the Whole Fractions Model for Fraction a. Sample: Circle 5 — 8 b. Circle 3 — 4 , 5 — 12 , 4 — 6 c. Rectangle 3 — 5 , 4 — 5 , 7 — 10 d. Counters 1 — 2 , 3 — 8 , 3 — 4 e. Piece of paper 7 — 8 , 1 — 8 , 1 — 4 Work with a partner. Add or subtract. Then check your answer by using one of the models in Activity 1 to estimate the sum or difference. a. Sample: 1 — 6 + 1 — 4 = 2 — 12 + 3 — 12 Write with common denominator. = 2 + 3 — 12 Add numerators. = 5 — 12 Simplify. b. 1 — 3 + 1 — 4 c. 5 — 8 + 1 — 3 d. 7 — 8 − 1 — 3 e. 2 — 3 − 4 — 9 ACTIVITY: Estimating Sums and Differences 2 2 Sum is less than one half.
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Fractions and Estimation - Big Ideas Math 2.1 Fractions and Estimation 49 33. RACECAR The height of a racecar is 46 7 — 8 inches. A model of the racecar is 2 7 — 9 inches tall.
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44 Chapter 2 Multiplying and Dividing Fractions
How can you use estimation to check that
your answer is reasonable?STATE STANDARDS
MA.6.A.5.3
S
Fractions and Estimation2.1
Work with a partner. Use the model for the whole to draw a model for the given fractions.
ACTIVITY: Using Models for Fractions11
WholeModel for the Whole
FractionsModel for Fraction
a. Sample: Circle 5
— 8
b. Circle 3
— 4
, 5
— 12
, 4
— 6
c. Rectangle 3
— 5
, 4
— 5
, 7
— 10
d. Counters 1
— 2
, 3
— 8
, 3
— 4
e. Piece of paper 7
— 8
, 1
— 8
, 1
— 4
Work with a partner. Add or subtract. Then check your answer by using one of the models in Activity 1 to estimate the sum or difference.
a. Sample:
1
— 6
+ 1
— 4
= 2
— 12
+ 3
— 12
Write with common denominator.
= 2 + 3
— 12
Add numerators.
= 5
— 12
Simplify.
b. 1
— 3
+ 1
— 4
c. 5
— 8
+ 1
— 3
d. 7
— 8
− 1
— 3
e. 2
— 3
− 4
— 9
ACTIVITY: Estimating Sums and Differences22
Sum is less thanone half.
Section 2.1 Fractions and Estimation 45
Use what you learned about estimation to complete Exercises 7–14 on page 48.
Work with a partner. Use a fraction model to choose 0, 1
— 4
, 1
— 2
, 3
— 4
, or 1 as the best estimate of the product.
a. Sample: 2
— 3
× 7
— 8
So, the best estimate is 1
— 2
.
b. 1
— 5
× 3
— 10
c. 3
— 4
× 5
— 7
d. 7
— 8
× 7
— 8
ACTIVITY: Estimating Products33
78
13
of 78
13
of
78
23
of
78
13
of
Shade of a model.78
The product is a little more than .12
78
Work with a partner. Use a fraction model to choose 0, 1
— 4
, 1
— 2
, 3
— 4
, or 1 as the best estimate of the quotient.
a. Sample: 5
— 9
÷ 2
So, the best estimate is 1
— 4
.
b. 3
— 5
÷ 3 c. 1
— 2
÷ 8 d. 5
— 6
÷ 2
ACTIVITY: Estimating Quotients44
Shade of a model.59
The quotient is about .14
Divide the shaded region into 2 parts.
5. IN YOUR OWN WORDS How can you use estimation to check that your answer is reasonable? Give some examples.
Lesson2.1
46 Chapter 2 Multiplying and Dividing Fractions
Key Vocabularyunderestimate, p. 47overestimate, p. 47compatible numbers, p. 47
Estimate the product by rounding to 0, 1
— 2
, or 1.
a. 3
— 8
× 11
— 12
b. 4
— 5
× 1
— 6
3
— 8
× 11
— 12
≈ 1
— 2
× 1 = 1
— 2
4
— 5
× 1
— 6
≈ 1 × 0 = 0
3
— 8
× 11
— 12
is about 1
— 2
. 4
— 5
× 1
— 6
is about 0.
EXAMPLE Estimating Products11
0 1
is close to .38
12 is close to 1.11
12
12
0 112
is close to 0.16 is close to 1.4
5
EXAMPLE Estimating with Mixed Numbers22Estimate the product or quotient by rounding each mixed number to the nearest whole number.
a. 5 1
— 4
× 3 9
— 10
b. 11 5
— 6
÷ 2 2
— 3
5 1
— 4
× 3 9
— 10
≈ 5 × 4 = 20 11 5
— 6
÷ 2 2
— 3
≈ 12 ÷ 3 = 4
5 1
— 4
× 3 9
— 10
is about 20. 11 5
— 6
÷ 2 2
— 3
is about 4.
Estimate the product or quotient.
1. 1
— 9
× 4
— 5
2. 9
— 10
× 5
— 12
3. 2 7
— 8
× 6 1
— 3
4. 24 1
— 5
÷ 3 1
— 2
5 1 —
4 is closer to 5 than to 6.
3 9 —
10 is closer to 4 than to 3.
11 5 —
6 is closer to 12 than to 11.
2 2 —
3 is closer to 3 than to 2.
Exercises 7–22
Lesson Tutorials
ReadingThe symbol ≈ means “approximately equal to.”