# Fraction Benchmark Numbers

Videos, examples, and solutions to help Grade 5 students learn how to use fraction benchmark numbers to assess reasonableness of addition and subtraction equations.

Common Core Standards: 5.NF.1, 5.NF.2

New York State Common Core Math Grade 5, Module 3, Lesson 13

Download Worksheets for Grade 5, Module 3, Lesson 13 (Pdf)

Lesson 13 Application Problem
Mark jogged 3 5/7 km. His sister jogged 2 4/5 km. How much farther did Mark jog than his sister?

Lesson 13 Concept Development
Problem 1
1/2 + 3/4
Problem 2
1 2/5 - 2/3
Problem 3
4/10 + 2/3
Problem 4
4/10 + 2/9
Problem 5
1 4/7 - 9/10
Problem 6
4/5 - 1/8
Problem 7
2 1/3 + 3 1/5 _____ 6 + 7/8
Problem 8
4 9/10 - 1 1/8 ____ 2 1/2 + 2/7

Lesson 13 Problem Set

1. Are the following greater than or less than 1? Circle the correct answer.
a) 1/2 + 2/7, greater than 1 or less than 1
b) 5/8 + 3/5, greater than 1 or less than 1
c) 1 1/4 - 1/3, greater than 1 or less than 1
d) 3 5/8 - 2 5/9, greater than 1 or less than 1
2. Are the following greater than or less than 1/2? Circle the correct answer.
a) 1/4 + 2/3, greater than 1/2 or less than 1/2
b) 3/7 - 1/8, greater than 1/2 or less than 1/2
c) 1 1/7 - 7/8, greater than 1/2 or less than 1/2
d) 3/7 + 2/6, greater than 1/2 or less than 1/2
3. Use > , < , or = to make the following statements true.
a) 5 2/3 + 3 3/4 ____ 8 2/3
b) 4 5/8 - 3 2/5 ____ 1 5/8 + 2/5
c) 5 1/2 + 1 3/7 ____ 6 + 13/14
d) 15 4/7 - 11 2/5 ____ 4 4/7 + 2/5

Lesson 13 Homework
5. A tree limb hangs 5 1/4 feet from a telephone wire. The city trims back the branch before it grows within 2 1/2 feet of the wire. Will the city allow the tree to grow 2 3/4 more feet?
6. Mr. Kreider wants to paint two doors and several shutters. It takes 2 1/8 gallons of paint to coat each door and 1 3/5 gallons of paint to coat his shutters. If Mr. Kreider buys three 2-gallon cans of paint, does he have enough to complete the job?

Lesson 13 Homework

This video shows how to estimate the reasonableness of sums and differences of fractions by comparing them to zero, one half, and one whole.

1. Are the following greater than or less than 1? Circle the correct answer.
a) 1/2 + 4/9 is greater than 1 or less than 1
2. Are the following greater than or less than 1/2? Circle the correct answer.
e) 1/5 + 1/4 is greater than 1/2 or less than 1/2
3. Use > , < , or = to make the following statements true.
i) 5 4/5 + 2 2/3 _____ 8 3/4
j) 3 4/7 - 2 3/5 _____ 1 4/7 + 3/5

Lesson 13 Homework

1. Are the following greater than or less than 1? Circle the correct answer.
a) 1/2 + 4/9 is greater than 1 or less than 1
d) 4 3/5 - 3 3/4 is greater than 1 or less than 1

2. Use > , < , or = to make the following statements true.
i) 5 4/5 + 2 2/3 _____ 8 3/4
j) 3 4/7 - 2 3/5 _____ 1 4/7 + 3/5

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.