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Arithmetic Addition and subtraction Properties of equalityHere you will learn how to multiply multi digit numbers with strategies, such as the relationship between addition and subtraction, the properties of operations, and how to use the standard algorithm.
Students will first learn about multiplying multi digit numbers in 4 th grade and learn to use the standard algorithm to multiply in 5 th grade.
Multiplying multi digit numbers is multiplying large numbers together and finding their product.
When first working with multi-digit multiplication, the focus is on using strategies including place value understanding, properties of operations and the relationship between multiplication and division.
For example,
20 \times 61= \; ?
Notice there are many ways to solve the same problem – using partial products, using the distributive property and area models. Knowing the names of each strategy is not important, but understanding why they work and making connections between them is.
After students have had sufficient practice understanding division with mostly single-digit numbers in 3 rd grade and multi-digit whole numbers in 4 th, the standard algorithm is taught in 5 th grade.
For example,
20 \times 61= \; ?
Start by writing the column multiplication equation. Leave an empty row at the top.
First, multiply the top number by the ones place in the bottom number (multiplier).
This shows that 20 \times 1=20
Then multiply the top number by the tens place of the bottom number (multiplier).
Since the 6 in 61 represents 60, we place a 0 in the ones position as a place holder.
This shows that 60 \times 20=1,200
Notice that since multiplying 6 \times 2=12 produces 2 digits in the product, this step requires regrouping. You record the 2 and regroup the 1 to the next position – in this case the thousands.
Finally, add the partial products for the final answer.
So 20 \times 61=1,220.
Note: This page does not cover multiplication with decimals. However, students use strategies in fifth grade to multiply decimals up to hundredths and use the standard algorithm in 6th grade to multiply all decimals.
See also: Multiplying and dividing decimals
How does this apply to 4 th grade math and 5 th grade math?
Use this worksheet to check your grade 4 studentsβ understanding of multiplying multi-digit numbers. 15 questions with answers to identify areas of strength and support!
DOWNLOAD FREEUse this worksheet to check your grade 4 studentsβ understanding of multiplying multi-digit numbers. 15 questions with answers to identify areas of strength and support!
DOWNLOAD FREEIn order to multiply multi digit numbers with strategies:
Solve 19 \times 8
19 \times 8= \; ?
2Choose a solving strategy.
19 \times 8 is one group of 8 less than 20 \times 8. You can use this related fact to solve.
3Solve the equation.
20 \times 8=160 and 160-8=152.
So 19 \times 8=152.
Solve 238 \times 6.
Write the multiplication equation.
238 \times 6= \; ?
Choose a solving strategy.
You can use an area model to solve.
Solve the equation.
So 238 \times 6=1,428.
There are 81 classroom novel sets. Each novel set has 34 books. How many books are there in all the sets?
Write the multiplication equation.
There are 81 groups of 34, which is written asβ¦
34 \times 81= \; ?
Choose a solving strategy.
You can use partial products to solve.
Solve the equation.
34 \times 81
=(4+30) \times 81 \quad **Break 34 up into 4 + 30 and multiply both by 81
=4 \times 81+30 \times 81
=324+30 \times(80+1) \quad **Break 81 up into 80 + 1 and multiply both by 30
=324+2,400+30
=2,754
So 34 \times 81=2,754
In order to multiply multi digit numbers with the standard algorithm:
Solve 34 \times 7 using the standard algorithm.
Write the column multiplication equation.
Start by writing the column multiplication equation. Leave an empty row at the top.
Multiply the top number by the ones position of the bottom number (multiplier) – recording the partial product.
First, multiply the top number by the ones place in the bottom number (multiplier).
Notice that since multiplying 7 \times 4=28 produces 2 digits in the product, this step requires regrouping. You record the ones digit and regroup the tens digit to the next position.
Notice that we add the regrouped 2 after multiplying: 3 \times 7=21 and 21+2=23.
Repeat for each position in the multiplier.
7 is the only digit in the multiplier – so there is nothing to repeat.
Add all the partial products together.
There are no partial products. The final answer is shown.
34 \times 7=238.
Solve 281 \times 5 using the standard algorithm.
Write the column multiplication equation.
Start by writing the column multiplication equation. Leave an empty row at the top.
Multiply the top number by the ones position of the bottom number (multiplier) – recording the partial product.
First, multiply the top number by the ones place in the bottom number (multiplier).
Repeat for each position in the multiplier.
5 is the only digit in the multiplier – so there is nothing to repeat.
Add all the partial products together.
There are no partial products. The final answer is shown.
281 \times 5=1,405.
Solve 37 \times 19 using the standard algorithm.
Write the column multiplication equation.
Start by writing the column multiplication equation. Leave an empty row at the top.
Multiply the top number by the ones position of the bottom number (multiplier) – recording the partial product.
First, multiply the top number by the ones place in the bottom number (multiplier).
This shows that 9 \times 37=333.
Repeat for each position in the multiplier.
Next, multiply the top number by the tens place in the bottom number (multiplier).
Since the 1 in 17 is in the tens place, remember to put 0 as a place holder in the ones column.
This shows that 10 \times 37=370.
Add all the partial products together.
The final product is 37 \times 19=703.
1. Solve 88 \times 3.
You can use a related fact to solve.
88 \times 3 is two groups of 3 less than 90 \times 3.
90 \times 3=270
and
270-3-3=264.
So 88 \times 3=264.
2. Solve 801 \times 9.
Break up 801 into parts \rightarrow 801=800+1.
Since ββ 800 \times 9=7,200 and 1 \times 9=9. This meansβ¦
\begin{aligned} & 801 \times 9 \\\\ & =(800+1) \times 9 \\\\ & =(800 \times 9)+(1 \times 9) \\\\ & =7,200+9 \\\\ & =7,209 \end{aligned}
3. Each recipe calls for 18 ounces of fruit. Jeylani wants to make 33 recipes. How many ounces of fruit does she need?
Use an area model to solve.
4. Solve 76 \times 4 with the algorithm.
Notice that since multiplying 6 \times 4=24 produces 2 digits in the product, this step requires regrouping.
Notice that we added the regrouped 2 after multiplying: 4 \times 8=28 and 28 + 2 = 30.
5. Solve 925 \times 4 with the algorithm.
6. An English teacher requires his students to read 45 minutes each night. How many total minutes will each student have read after 41 nights?
In third grade, students work with multiplying one-digit numbers within 100. Their work with multiplication is directly connected to their work with division.
Students extend their work in fourth grade to multi-digit multiplication by multiplying 2- digit numbers, 3- digit numbers and 4- digit numbers.
In 5 th grade, they learn how to solve problems with the standard algorithm. In all three grade levels, students use their reasoning and understanding of numbers and multiplication to solve.
It is important to note that there are additional standards where students focus on how to multiply by 10, 100, etc., through place value understanding. This work comes before learning how to multiply with other larger numbers.
Students begin multiplying fractions by whole numbers in 4 th grade, in both mathematical and real world contexts. Students expand to multiply fractions by fractions in 5 th grade – using strategies and algorithms.
This is also when they begin to multiply with decimals – but only using strategies and place value understanding. Students learn the algorithm to multiply with decimals in 6 th grade.
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Prepare for math tests in your state with these 3rd Grade to 8th Grade practice assessments for Common Core and state equivalents.
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