Place Values
Thousands, hundreds, tens, ones, tenths, hundredths
Start here
How to Use These Lessons
Read the short explanation, follow the worked example, then try the practice problems. If one part feels tricky, go slowly and write each step on paper.
- Say what the problem is asking.
- Choose the operation or rule.
- Work neatly from left to right or top to bottom.
- Check that the answer makes sense.
Operation Words
Altogether, left, groups of, shared equally, difference
Check Work
Estimate first, use the opposite operation, and reread the question
1
Place Value and Comparing Numbers
Place value tells how much a digit is worth based on where it sits. In 4,582, the 4 means four thousands, the 5 means five hundreds, the 8 means eight tens, and the 2 means two ones.
- Start comparing at the largest place value.
- Use >, <, and = to compare numbers.
- A zero can hold a place even when there are none of that value.
Example: Which is greater, 6,304 or 6,340?
Both have 6 thousands and 3 hundreds. Compare the tens: 0 tens is less than 4 tens. So 6,340 is greater.
Practice
- Write 7,219 in expanded form.
- Compare 8,405 and 8,450 using >, <, or =.
- What is the value of the 6 in 3,681?
2
Addition with Regrouping
Addition means putting groups together. Line up the ones, tens, hundreds, and thousands. Add from right to left so regrouping lands in the next place.
Step 1Add the ones.
Step 2Carry a ten if the sum is 10 or more.
Step 3Keep moving left until every place is added.
Example: 2,478 + 1,365
Ones: 8 + 5 = 13, write 3 and carry 1. Tens: 7 + 6 + 1 = 14, write 4 and carry 1. Hundreds: 4 + 3 + 1 = 8. Thousands: 2 + 1 = 3. The answer is 3,843.
Practice
- 325 + 248
- 1,469 + 2,308
- 4,096 + 875
3
Subtraction with Borrowing
Subtraction means taking away or finding the difference. When the top digit is too small, borrow from the next place value and trade it for 10 of the smaller place.
Example: 502 - 278
Borrow so the ones become 12. Then 12 - 8 = 4. Borrow for the tens so 9 - 7 = 2. Finally, 4 - 2 = 2. The answer is 224.
Check: Add the answer to the number you subtracted. 224 + 278 = 502.
Practice
- 731 - 456
- 900 - 367
- 5,012 - 2,849
4
Multiplication Facts and Larger Products
Multiplication is repeated addition. A product is the answer to a multiplication problem. Knowing facts like 6 x 8 = 48 helps with larger numbers.
Example: 24 x 6
Break 24 into 20 and 4. Then 20 x 6 = 120 and 4 x 6 = 24. Add 120 + 24 = 144.
6 x 6 = 36
6 x 7 = 42
6 x 8 = 48
6 x 9 = 54
Practice
- 7 x 9
- 32 x 4
- 18 x 5
5
Division and Remainders
Division means sharing equally or making equal groups. Sometimes there is an amount left over. That leftover amount is called a remainder.
Example: 43 / 5
5 goes into 43 eight times because 5 x 8 = 40. There are 3 left over, so the answer is 8 remainder 3.
Check: Multiply the divisor by the quotient, then add the remainder. 5 x 8 + 3 = 43.
Practice
- 56 / 7
- 39 / 4
- 72 / 9
6
Fractions
A fraction shows part of a whole. The bottom number is the denominator; it tells how many equal parts make the whole. The top number is the numerator; it tells how many parts you have.
Example: 3/4
If a sandwich is cut into 4 equal parts and you eat 3 parts, you ate 3/4 of the sandwich.
Practice
- Which is larger, 1/2 or 1/4?
- Write the fraction for 5 shaded parts out of 8 equal parts.
- What is 2/6 simplified?
7
Decimals and Money
Decimals are another way to show parts of a whole. Money uses decimals because one dollar is split into 100 cents.
Example: $3.75 + $2.40
Line up the decimal points. Add cents to cents and dollars to dollars: 3.75 + 2.40 = 6.15.
- Tenths are the first place after the decimal point.
- Hundredths are the second place after the decimal point.
- When adding or subtracting decimals, keep decimal points lined up.
Practice
- $4.25 + $1.30
- 7.6 - 2.4
- Which is greater, 0.8 or 0.75?
8
Measurement and Time
Measurement tells how long, heavy, or full something is. Time problems often ask you to add or subtract minutes and hours.
Length12 inches = 1 foot
Time60 minutes = 1 hour
Weight16 ounces = 1 pound
Example: A movie starts at 2:15 and lasts 1 hour 30 minutes.
Add 1 hour to get 3:15. Add 30 minutes to get 3:45.
Practice
- How many inches are in 3 feet?
- What time is 45 minutes after 10:20?
- How many ounces are in 2 pounds?
9
Shapes, Perimeter, and Area
Perimeter is the distance around a shape. Area is the space inside a flat shape. Rectangles are a good place to begin because their sides come in equal pairs.
8 cm
3 cm
Example: A rectangle is 8 cm long and 3 cm wide.
Perimeter: 8 + 3 + 8 + 3 = 22 cm. Area: 8 x 3 = 24 square cm.
Practice
- Find the perimeter of a square with sides of 6 inches.
- Find the area of a rectangle that is 9 feet by 4 feet.
- How many sides does a hexagon have?
10
Word Problems
Word problems are stories with math inside. Read carefully, underline the numbers, and decide what the question is asking before you calculate.
Addaltogether, total, in all, combined
Subtractleft, fewer, difference, gave away
Multiplygroups of, each, rows of, times
Divideshared equally, split, per group
Example: Sam has 4 bags with 6 marbles in each. How many marbles does Sam have?
The words "in each" tell us there are equal groups. Multiply 4 x 6 = 24.
Practice
- Lena has 18 stickers and buys 27 more. How many stickers does she have now?
- A class has 30 students. Six are absent. How many are present?
- There are 5 boxes with 9 crayons in each box. How many crayons are there?
Check your work
Answer Key
- 7,000 + 200 + 10 + 9; 8,405 < 8,450; 600
- 573; 3,777; 4,971
- 275; 533; 2,163
- 63; 128; 90
- 8; 9 remainder 3; 8
- 1/2; 5/8; 1/3
- $5.55; 5.2; 0.8
- 36 inches; 11:05; 32 ounces
- 24 inches; 36 square feet; 6 sides
- 45 stickers; 24 students; 45 crayons