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Adding & subtracting two 2-digit numbers

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visibility 80update 2 months agobookmarkshare

In this topic you will

Add two $2$-digit numbers.
Subtract a $2$-digit number from another $2$-digit number.
Find the difference between two $2$-digit numbers.

Key Words

swap
total

Show Definitions

swap: To change the order of two numbers or objects, so the first becomes the second and the second becomes the first.
total: The whole amount altogether, usually found by adding parts together.

You will add or subtract numbers almost every day for lots of reasons. This unit helps you to add and subtract tens and ones in the same calculation.

EXERCISES

Exercise $1.11$

$1$. Add two $2$-digit numbers.
Use some objects on the place value grid to help you calculate.

a. $21 + 47$

b. $35 + 62$

c. $54 + 32$

d. $64 + 25$

e. $71 + 16$

f. $46 + 32$

Place value grid labelled tens and ones to help calculate the additions

👀 Show answer

a.$21 + 47 = 68$

b.$35 + 62 = 97$

c.$54 + 32 = 86$

d.$64 + 25 = 89$

e.$71 + 16 = 87$

f.$46 + 32 = 78$

Worked example

$67 - 32 =$ ________

Place value grids with tens and ones beans showing 67 then crossing out 32, plus working bubbles and calculation steps

Answer:

$67 - 32 = 35$

Method: Split each number into tens and ones.

$67 = 60 + 7$ and $32 = 30 + 2$.

Subtract the tens, then the ones:

$60 - 30 = 30$ and $7 - 2 = 5$.

$30 + 5 = 35$, so $67 - 32 = 35$.

EXERCISES

$2$. Solve each number sentence. Show your steps.

a. $58 - 35$

b. $76 - 41$

c. $67 - 26$

👀 Show answer

a.$58 - 35$

$58 = 50 + 8$, $35 = 30 + 5$

$50 - 30 = 20$, $8 - 5 = 3$, so $20 + 3 = 23$.

b.$76 - 41$

$76 = 70 + 6$, $41 = 40 + 1$

$70 - 40 = 30$, $6 - 1 = 5$, so $30 + 5 = 35$.

c.$67 - 26$

$67 = 60 + 7$, $26 = 20 + 6$

$60 - 20 = 40$, $7 - 6 = 1$, so $40 + 1 = 41$.

$3$. Complete each subtraction.
Use some objects on the place value grid to help you calculate.

a. $89 - 52$

b. $56 - 44$

c. $78 - 36$

d. $67 - 24$

Blank place value grid labelled tens and ones to help complete the subtractions

👀 Show answer

a.$89 - 52 = 37$

b.$56 - 44 = 12$

c.$78 - 36 = 42$

d.$67 - 24 = 43$

$4$. Use the $100$ square to help you add or subtract to find the missing numbers.

a. $34 + 21 =$ ________

b. $87 - 43 =$ ________

c. $69 - 35 =$ ________

d. $47 + 32 =$ ________

100-square grid from 1 to 100 with a tip box to count on tens and ones to add or subtract

👀 Show answer

a.$34 + 21 = 55$

b.$87 - 43 = 44$

c.$69 - 35 = 34$

d.$47 + 32 = 79$

$5$.

a. Subtract a number in the second cloud from a number in the first cloud.
Write your number sentence.
Which method will you use?
Do this $3$ times.

b. Which calculation will give you the greatest answer?

c. Which calculation will give you the smallest answer?

Two number clouds: first cloud has 79, 56, 68, 87 and second cloud has 25, 11, 43, 32

👀 Show answer

a. Example answers (any $3$ correct number sentences are fine):

$79 - 25 = 54$
$68 - 32 = 36$
$87 - 11 = 76$

A good method is to split into tens and ones (for example $79 = 70 + 9$ and $25 = 20 + 5$) and subtract tens, then ones.

b. Use the largest number from the first cloud and the smallest from the second cloud:
$87 - 11 = 76$ (greatest answer).

c. Use the smallest number from the first cloud and the largest from the second cloud:
$56 - 43 = 13$ (smallest answer).

Think like a Mathematician

Choose a number from the grid.

Swap the digits in the number to make a new number.

Add the two numbers together.

For example: $35 + 53 = 88$.

What do you notice? Can you explain why this happens? Discuss what you notice with your partner or in a small group.

Number grid showing 14–16, 24–26, 34–36 to choose a number from for swapping digits

Show Answers

What do you notice? When you swap the digits and add, the total is always a multiple of $11$. For example: $14 + 41 = 55$, $26 + 62 = 88$, $36 + 63 = 99$.
Why does this happen? Let the number be $10a + b$ (tens digit $a$, ones digit $b$). Swapping gives $10b + a$. Adding: $(10a + b) + (10b + a) = 11a + 11b = 11(a + b)$, which is always a multiple of $11$.
Discussion (solo version): Try at least $3$ different numbers from the grid and record your totals. Write one sentence explaining the pattern you found.

EXERCISES

$6$. Sofia made some mistakes when she wrote these number facts.
Tick those that are correct.
Correct any that are not equivalent in value.

$24 + 35 = 22 + 36$

$45 + 54 = 44 + 55$

$67 - 23 = 68 - 25$

$56 - 35 = 58 - 37$

👀 Show answer

Correct:$45 + 54 = 44 + 55$ and $56 - 35 = 58 - 37$.

Not correct:$24 + 35 = 22 + 36$ and $67 - 23 = 68 - 25$.

One way to correct them:

$24 + 35 = 23 + 36$
$67 - 23 = 68 - 24$

$7$. Find the difference between each pair of numbers.
Write the number sentence.
Use a number line or a $100$ square to help you.

Pairs of numbers (49 and 32), (65 and 87), (54 and 68) shown above a 100-square and a 0–100 number line

👀 Show answer

$49 - 32 = 17$

$87 - 65 = 22$

$68 - 54 = 14$

$8$. The difference between two numbers is $14$.
If one of the numbers is $45$, what could the other number be?
Did you get the same answer as your partner?
Is there more than one possible answer?

👀 Show answer

Two possible answers are:

$45 - 14 = 31$
$45 + 14 = 59$

Yes, there is more than one possible answer.

What we've learned

We learned how to add two $2$-digit numbers by separating them into tens and ones.
We learned how to subtract a $2$-digit number from another $2$-digit number using place value.
We used number lines and a $100$ square to help us calculate differences.
We understood that the difference between two numbers can be found by counting on or subtracting.
We explored how adjusting numbers in addition and subtraction can keep the total or difference the same (equivalent number facts).

Adding & subtracting two 2-digit numbers

In this topic you will

Key Words

EXERCISES

EXERCISES

Think like a Mathematician

EXERCISES

What we've learned

Related Past Papers

Related Tutorials

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