Decimals
12.25 plus 1.5
13.75
2 × (3 + 4) + 5
2 × 7 = 14
Then:
14 + 5 = 19
✅ Answer: 19
x − 4 + 2 = 9
Steps:
Combine like terms on the left:
x − 2 = 9
Add 2 to both sides:
x = 11
✅ Answer: x = 11
The ratio of red balls to blue balls is 8:12. Simplify this ratio.
Solution:
Divide both by 4 → 8 ÷ 4 : 12 ÷ 4 = 2:3
1/3 + 1/4
Steps:
Common denominator = 12
4/12 + 3/12 = 7/12
Answer:
7/12
9.15 − 3.8
5.35
(8 − 3)²
Steps: (5)² = 25
✅ Answer: 25
0.4x − 1.2 = 2.8
Steps:
Add 1.2 to both sides:
0.4x = 4.0
Divide both sides by 0.4:
x = 10
✅ Answer: x = 10
The ratio of cats to dogs is 2:3. If there are 15 dogs, how many cats are there?
Solution:
Set up proportion:
2 / 3 = x / 15
Cross multiply: 3x = 2 × 15 = 30
x = 30 ÷ 3 = 10 cats
5/6 - 1/8
Common denominator = 24
20/24 - 3/24 = 17/24
Answer:
17/24
3.75 × 2.4
9.0
6 + 4 × (2 + 1)
Steps: 6 + 4 × 3 → 6 + 12 = 18
✅ Answer: 18
−2(x − 5) + 3 = 1
Steps:
Distribute: −2x + 10 + 3 = 1
Combine like terms: −2x + 13 = 1
Subtract 13: −2x = −12
Divide by −2: x = 6
✅ Answer: x = 6
The ratio of red cars to blue cars is 4:7. If there are 28 blue cars, how many red cars are there?
Solution:
Set up proportion:
4 / 7 = x / 28
Cross multiply:
7x = 4 × 28 = 112
Divide both sides by 7:
x = 112 ÷ 7 = 16
✅ Answer: 16 red cars
6/8 - 1/3
Common denominator = 24
18/24 - 8/24 = 10/24
Simplify 10/24 → 5/12
Answer:
5/12
12.5 × 0.08
1.0
(12 ÷ 3) + 2² × 3
4 + 4 × 3 → 4 + 12 = 16
✅ Answer: 16
3(x + 4) = 2x + 18
Steps:
Distribute left: 3x + 12 = 2x + 18
Subtract 2x from both sides: x + 12 = 18
Subtract 12: x = 6
✅ Answer: x = 6
The ratio of boys to girls in a class is 2:3. There are 25 students total. How many boys and girls are there?
Solution:
Total parts = 2 + 3 = 5
One part = 25 ÷ 5 = 5
Boys = 2 × 5 = 10
Girls = 3 × 5 = 15
3/4 + 2/6
Steps:
Common denominator = 12
(3/4) = 9/12
(2/6) = 4/12
Add: 9/12 + 4/12 = 13/12
Simplify: 13/12 = 1 1/12
Answer:
1 1/12
15.75 ÷ 1.5
10.5
18 ÷ (3 × 2) + 5² − (4 + 1)
3 × 2 = 6 → 18 ÷ 6 = 3
5² = 25
4 + 1 = 5
→ 3 + 25 − 5 = 23
✅ Answer: 23
4(x + 2) − 3 = 2(2x + 5) − 1
Steps:
Distribute both sides:
Left: 4x + 8 − 3 = 4x + 5
Right: 4x + 10 − 1 = 4x + 9
Simplify both sides:
4x + 5 = 4x + 9
Subtract 4x from both sides:
5 = 9. ✅ Answer: No solution
The ratio of cats to dogs in a shelter is 5:8. If there are 40 cats, how many dogs are there?
Solution:
Set up proportion:
5 / 8 = 40 / x
Cross multiply:
5x = 8 × 40 = 320
Divide both sides by 5:
x = 320 ÷ 5 = 64
✅ Answer: 64 dogs
4/8 + 3/6 - 1/3
Common denominator = 24
(4/8) = 12/24
(3/6) = 12/24
(1/3) = 8/24
Calculate: 12/24 + 12/24 - 8/24 = 16/24
Simplify 16/24:
Divide numerator and denominator by 8 → 2/3
Answer:
2/3