We included HMH Into Math Grade 4 Answer Key PDF Module 4 Lesson 5 Use Mental Math Strategies for Multiplication and Division to make students experts in learning maths.
HMH Into Math Grade 4 Module 4 Lesson 5 Answer Key Use Mental Math Strategies for Multiplication and Division
I Can use properties of operations and the relationship between multiplication and division to find products and quotients using mental math.
Step It Out
1. James crochets a pattern with this yarn. Each color has 7 rows with 50 stitches in each row. How many stitches are in the pattern?
Find 4 × 7 × 50.
A. Use the Commutative Property.
4 × 7 × 50 = 4 × ___ × 7
Answer:
4 × 50 × 7
Connect to Vocabulary
The Commutative Property of Multiplication states that when the order of the factors is changed, the product is the same.
B. Use basic facts and place value to multiply two factors.
Think: 4 × 5 = 20, so 4 × 50 = ___
Answer:
4 x 50 = 200
C. Multiply the result by the third factor.
4 × 50 × 7 = ___ × 7 = ____
There are ___ stitches in the pattern.
Answer:
4 × 50 × 7 = 200 × 7 = 1400
2. Find 325 ÷ 5.
A. Use addition. Break the dividend into two parts that divide easily by 5.
325 ÷ 5 = (__ + ___) ÷ 5
Answer:
325 ÷ 5 = (300+ 25) ÷ 5
B. Divide each part and then add the two quotients.
325 ÷ 5 = (300 ÷ 5) + (25 ÷ 5)
= ___ + ____ = _____
Answer:
60 + 5
= 65
Step It Out
Question 3.
Mei has 800 craft sticks for 4 projects. How many craft sticks can she use for each project?
Find 800 ÷ 4.
A. Use the relationship between multiplication and division.
Think: What number when multiplied by ___ equals 800?
Answer:
4 x 2 = 8
B. Use basic facts and place value to solve.
Think: 4 × 2 = 8, so 4 × ___ = 800.
800 ÷ 4 = ____
Answer:
4 × 2 = 8, so 4 × 200 = 800.
800 ÷ 4 = 200
Each project can use 200 craft sticks.
4. Find 5 × 72.
A. Use place value to rewrite the equation.
5 × 72 = 5 × (__ + ___)
Answer:
5 × 72 = 5 × (70+ 2)
Connect to Vocabulary
The Distributive Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
B. Use the Distributive Property and solve.
5 × 72 = (5 × ____)
= ____ + ______
= ______
Answer:
5 x 72 = (5 x 70 + 5 x 2)
= 350 + 20
= 370
Turn and Talk What other strategies can you use to multiply and divide with mental math?
Explanation:
Compatible numbers are pairs of numbers that are easy to add, subtract, multiply, or divide mentally.
Check Understanding Math Board
Use mental math to find the product or the quotient.
Question 1.
30 × 8 × 2 = ____
Answer:
8 x 3 = 24
24 x 2 = 48
30 × 8 × 2 = 480
Explanation:
The Commutative Property of Multiplication states that when the order of the factors is changed, the product is the same.
Question 2.
450 ÷ 5 =
Answer:
450 ÷ 5 = 90
Explanation:
9 x 5 = 45
Distributive property means dividing the given operations on the numbers so that the equation becomes easier to solve. The distributive property definition simply states that “multiplication distributed over addition.”
On Your Own
Use mental math to find the product or the quotient. Tell which strategy you used.
Question 3.
20 × 9 × 5
Answer:
20 × 9 × 5 = 900
Explanation:
5 x 2 = 10
9 x 10 = 90
The Commutative Property of Multiplication states that when the order of the factors is changed, the product is the same.
Question 4.
8,800 ÷ 8
Answer:
8800 ÷ 8 = 1100
Explanation:
8 x 1 = 8
Distributive property means dividing the given operations on the numbers so that the equation becomes easier to solve. The distributive property definition simply states that “multiplication distributed over addition.”
Question 5.
342 ÷ 6
Answer:
342 ÷ 6 = 57
Explanation:
Distributive property means dividing the given operations on the numbers so that the equation becomes easier to solve. The distributive property definition simply states that “multiplication distributed over addition.”
Question 6.
7 × 48
Answer:
7 × 48 = 336
Explanation:
The Commutative Property of Multiplication states that when the order of the factors is changed, the product is the same.
Question 7.
Melissa works at a pet store that sells aquarium fish. She puts 120 fish into 4 different tanks. Melissa puts the same number of fish in each tank. How many fish are in each tank?
Find 120 ÷ 4.
Answer:
120 ÷ 4 = 30
Explanation:
4 x 3 = 12
30 fish are in each tank
Question 8.
Jordan makes 4 beaded necklaces. Each necklace has 36 beads. How many beads does Jordan use to make the necklaces? Find 4 × 36.
_____________
Answer:
4 x 36 = 144
Explanation:
4 x 36 = (4 x 30 + 4 x 6)
= 120 + 24
= 144
On Your Own
Use mental math to find the product or the quotient. Tell which strategy you used.
Question 9.
James and Michael each buy 6 of these packages of small toy dinosaurs. How many toy dinosaurs do James and Michael buy?
Find 2 × 6 × 15.
_______________
Answer:
2 × 6 × 15 = 180
Explanation:
2 x 6 = 12
12 x (10 + 5)
12 x 10 + 12 x 5
= 120 + 60
= 180
Question 10.
A scientist counts 1,600 birds in an area covering 8 square miles of rainforest. About how many birds are in each square mile?
Find 1,600 ÷ 8.
Answer:
1,600 ÷ 8 = 200
Explanation:
8 x 2 = 16
200 birds are in each square mile
Question 11.
STEM On a cold night, a hummingbird will go into a sleep-like state to save energy. In this state, the bird’s heart rate can slow to around 55 beats per minute. If a hummingbird is in this sleep-like state for 8 minutes, how many times will it’s heart beat?
Find 8 × 55.
_____________
Answer:
Explanation:
8 x (50 + 5)
(8 x 50 + 8 x 5)
= 400 + 40
= 440
Question 12.
Open Ended Alan uses halving and doubling to find 240 ÷ 6. What is another way he could find the quotient?
Answer:
240 ÷ 6 = 40
Explanation:
6 x 4 = 24
Then we can add the left over zero to the answer.
This is the another way he can find.