Estimating Fraction Sums and Differences 4-9 Estimating Fraction Sums and Differences Course 1 Warm Up Problem of the Day Lesson Presentation

Write each sum or difference in simplest form. Warm Up Write each sum or difference in simplest form. 1. + 2. – 3. 2 + 1 4. 5 –1 3 8 __ 5 8 __ 9 10 __ 3 10 __ 3 5 __ 1 1 4 __ 1 4 __ 1 2 __ 3 8 9 __ 2 9 __ 2 3 __ 4

Problem of the Day Students at a school dance formed equal teams to play a game. When they formed teams of 3, 4, 5, or 6, there was always one person left. What is the smallest number of people that there could have been at the dance? 61, the LCM of all the numbers, plus 1

Learn to estimate sums and differences of fractions and mixed numbers.

1 2 __ You can estimate fractions by rounding to 0, , or 1. 2 __ 8 4 • 1 3 1 1 1 3 5 7 3 4 __ 1 2 __ The fraction is halfway between and 1, but we usually round up. So the fraction rounds to 1. 3 4 __

You can round fractions by comparing the numerator and denominator. 1 2 __ 1 • • closer to Each numerator is about half the denominator, so the fractions are close to . 1 2 __ closer to 1 Each numerator is about the same as the denominator, so the fractions are close to 1. closer to 0 Each numerator is much less than half the denominator, so the fractions are close to 0. 1 5 __ 2 11 __ 2 15 __ 5 11 __ 4 7 __ 9 20 __ 9 10 __ 16 19 __ 6 7 __ 1 2 __

Additional Example 1A: Estimating Fractions Estimate each sum or difference by rounding to 0, , or 1. + 1 2 __ 6 7 __ 3 8 __ 6 7 __ 3 8 __ 6 7 __ 3 8 __ 1 2 __ + Think: rounds to 1 and rounds to . 1 2 __ 1 2 __ 1 + = 1 6 7 __ 3 8 __ 1 2 __ + is about 1 .

Additional Example 1B: Estimating Fractions Estimate each sum or difference by rounding to 0, , or 1. – 1 2 __ 9 10 __ 7 8 __ 9 10 __ 7 8 __ 9 10 __ 7 8 __ – Think: rounds to 1 and rounds to 1. 1 – 1 = 0 9 10 __ 7 8 __ – is about 0.

Check It Out: Example 1A Estimate each sum or difference by rounding to 0, , or 1. + 1 2 __ 5 6 __ 3 7 __ 5 6 __ 3 7 __ 5 6 __ 3 7 __ 1 2 __ + Think: rounds to 1 and rounds to . 1 2 __ 1 2 __ 1 + = 1 5 6 __ 3 7 __ 1 2 __ + is about 1 .

Check It Out: Example 1B Estimate each sum or difference by rounding to 0, , or 1. – 1 2 __ 13 19 __ 2 11 __ 13 19 __ 2 11 __ – 2 11 __ 13 19 Think: rounds to 1 and rounds to 0. 1 – 0 = 1 13 19 __ 2 11 __ – is about 1.

two nearest whole numbers and the nearest . You can also estimate by rounding mixed numbers. You compare each mixed number to the two nearest whole numbers and the nearest . Does 10 round to 10, 10 , or 11? 1 2 __ 3 10 __ 1 2 __ 3 10 __ 1 2 __ 10 10 10 11 • 1 10 __ 2 10 __ 4 10 __ 6 10 __ 7 10 __ 8 10 __ 9 10 __ 10 10 10 10 10 10 10 3 10 __ 1 2 __ The mixed number 10 rounds to 10 .

Additional Example 2A: Sports Application The table shows the distances Tosha walked. About how far did Tosha walk on Tuesday and Thursday? 1 10 __ 7 8 5 + 4 5 + 5 = 10 She walked about 10 miles on Tuesday and Thursday.

Additional Example 2B: Sports Application The table shows the distances Tosha walked. About how much farther did Tosha walk on Sunday than Thursday? 9 10 __ 7 8 __ 8 – 4 9 – 5 = 4 She walked about 4 miles farther on Sunday than on Thursday.

Additional Example 2C: Sports Application The table shows the distances Tosha walked. Estimate the total distance Tosha walked on Thursday, Saturday, and Sunday. 7 8 __ 3 7 __ 9 10 __ 4 + 6 + 8 1 2 __ 1 2 __ 5 + 6 + 9 = 20 1 2 __ She walked about 20 miles on Thursday, Saturday, and Sunday.

Jerry’s Roller Skating Distances Check It Out: Example 2A The table shows the distances Jerry roller skated. About how far did Jerry skate on Tuesday and Sunday? Jerry’s Roller Skating Distances Distance (mi) 3 6 2 8 1 5 __ 7 Day Tuesday Thursday Saturday Sunday 1 5 __ 6 7 __ 3 + 2 3 + 3 = 6 He roller skated about 6 miles on Tuesday and Sunday.

Jerry’s Roller Skating Distances Check It Out: Example 2B The table shows the distances Jerry roller skated. About how much farther did Jerry skate on Saturday than Tuesday? Jerry’s Roller Skating Distances Distance (mi) 3 6 2 8 1 5 __ 7 Day Tuesday Thursday Saturday Sunday 1 7 __ 1 5 __ 8 – 3 8 – 3 = 5 He roller skated about 5 miles farther on Saturday than Thursday.

Jerry’s Roller Skating Distances Check It Out: Example 2C The table shows the distances Jerry roller skated. Estimate the total distance Tosha walked on Tuesday, Thursday, and Sunday. Jerry’s Roller Skating Distances Distance (mi) 3 6 2 8 1 5 __ 7 Day Tuesday Thursday Saturday Sunday 1 5 __ 3 + 6 + 2 6 7 3 1 2 __ 1 2 __ 3 + 6 + 3 = 12 1 2 __ He roller skated about 12 miles on Tuesday, Thursday, and Sunday.

Lesson Quiz: Part I Estimate each sum or difference by rounding to 0, , or 1. 1. 2. 3. 4. 1

Lesson Quiz: Part II 5. The conservation club picked up trash along the road for three weeks. The table shows the number of pounds of trash they collected. About how many pounds did they collect in weeks 2 and 3? about 37 pounds