Learn to multiply decimals by whole numbers using decimal grids and algorithm development!
Scenario: You're shopping for school supplies. Each pen costs $3.80, and you need to buy 12 pens. How much will you spend in total?
First, let's understand what 3.8 means using a decimal grid. We can think of 3.8 as 38 tenths (0.1).
3.8 = 38 tenths
38 out of 100 squares = 3.8
3.8 = 3 + 0.8 = 3 + 8/10 = 3 + 0.8
We need 12 groups of 3.8 each
Now let's calculate 12 × 3.8 using the decimal grid approach:
12 × 3.8 = 12 × (3 + 0.8)
Distributive property
= 12 × 3 + 12 × 0.8
Multiply each part
= 36 + 9.6 = 45.6
Add the results
Answer: You will spend $45.60 for 12 pens!
We can also use the standard multiplication algorithm, but we need to be careful about decimal places:
3.8
× 12
76 (3.8 × 2)
+ 380 (3.8 × 10)
45.6
First, multiply 38 × 12 = 456
3.8 has 1 decimal place, so result has 1 decimal place: 45.6
Let's verify our answer by breaking down the multiplication:
3.8 × 10 = 38.0
10 pens cost $38.00
3.8 × 2 = 7.6
2 pens cost $7.60
38.0 + 7.6 = 45.6
Total: $45.60 ✓
Let's estimate to check if our answer is reasonable:
3.8 ≈ 4 (round up)
Estimate: 4 × 12 = 48
Our answer: 45.6
Close to estimate ✓
You want to buy 8 notebooks at $2.50 each. How much will you spend?
2.5 × 8 = 20.0
Answer: $20.00
Calculate: 5.25 × 8
5.25 × 8 = 42.0
Calculate: 0.36 × 15
0.36 × 15 = 5.4
❌ 3.8 × 12 = 456 (WRONG!)
Forgot to place the decimal point
Correct: 3.8 × 12 = 45.6 (1 decimal place in the answer)
❌ 2.4 × 5 = 12.0 (Sometimes written as 12)
Both are correct, but 12.0 shows the decimal place
Remember: 12.0 = 12, but showing the decimal place helps with understanding