Adding Multiples of Ten (e.g., 40 + 30) - First Grade Mathematics
Welcome to the big leagues of addition! When you look at numbers like 40 and 30, they might look huge and intimidating at first. But here is the magnificent secret: adding multiples of ten is just as easy as adding single-digit numbers! Why? Because 40 + 30 is really just 4 tens plus 3 tens. If you know that 4 + 3 = 7, then you already know that 40 + 30 = 70! In this chapter, you will master adding round multiples of ten up to 100, use base-ten rods to prove your thinking, and unlock the mental power of place value.
What Is a Multiple of Ten?
A multiple of ten (also called a decade number) is any number that can be made using only complete rods or bundles of ten, with zero loose single units.
Multiples of Ten up to 90:
10 = 1 Ten
20 = 2 Tens
30 = 3 Tens
40 = 4 Tens
50 = 5 Tens
60 = 6 Tens
70 = 7 Tens
80 = 8 Tens
90 = 9 Tens
The Zero in the Ones Place
Notice that every multiple of ten ends with a 0. That zero is a placeholder that tells us: "There are zero loose ones here!"
The "Think Single Digits" Strategy
To add multiples of ten, look at the tens digits, add them just like single digits, and attach a zero to the ones place!
The Single-Digit Connection:
Single-Digit Fact: 4 + 3 = 7 (4 ones + 3 ones = 7 ones)
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Tens Fact: 4 Tens + 3 Tens = 7 Tens
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Multiples of Ten: 40 + 30 = 70!
Why This Works
Imagine you have 4 dimes and a friend gives you 3 dimes. How many dimes do you have? 4 dimes + 3 dimes = 7 dimes! Since each dime is worth 10 cents, 7 dimes is worth 70 cents. You are simply adding units of tens!
Modeling with Base-Ten Rods
Using base-ten blocks makes this strategy visible and impossible to forget.
Modeling 50 + 20 with Rods:
50 = 5 Rods: [==========] [==========] [==========] [==========] [==========]
20 = 2 Rods: [==========] [==========]
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Total Rods: 5 rods + 2 rods = 7 rods!
Value: 7 rods = 70!
Quick Sketch on Paper
To solve 50 + 20 on paper, draw 5 vertical lines for 50 (| | | | |) and 2 vertical lines for 20 (| |). Count all the lines: 7 lines! 7 tens equals 70.
Practice Exercises
Exercise 1: Solve 30 + 50. What basic single-digit fact helps you solve this problem?
Exercise 2: Solve these equations with multiples of ten mentally: 20 + 40 = __ 60 + 30 = __ 10 + 70 = __ 50 + 50 = __
Exercise 3: You have 4 rolls of pennies. Each roll holds 10 pennies. Your cousin gives you 2 more rolls of 10 pennies. How many pennies do you have in total? Write the equation with multiples of ten.
Exercise 4: Explain why 60 + 20 does not equal 800. What mistake would someone make to think the answer is 800?
Solutions and Explanations
Solution to Exercise 1: 30 + 50 = 80. The basic single-digit fact that helps is 3 + 5 = 8 (3 tens + 5 tens = 8 tens = 80).
Solution to Exercise 2: 20 + 40 = 60 60 + 30 = 90 10 + 70 = 80 50 + 50 = 100
Solution to Exercise 3: 4 rolls of 10 is 40 pennies, and 2 rolls of 10 is 20 pennies. The equation is 40 + 20 = 60 pennies in total.
Solution to Exercise 4: 60 + 20 equals 80 because you are combining 6 tens and 2 tens to get 8 tens. Someone who writes 800 mistakenly added an extra zero, confusing tens with hundreds. 8 tens is 80, not 800.