PEMDAS
SOLVE FOR X
Ratios
Fractions (must simplify)
Random!
100

12−4×(2+1)

Solution:


    • Parentheses first:
      2 + 1 = 3
      So the expression becomes:
      12 - 4 * 3

    • Multiplication next:
      4 * 3 = 12
      Now the expression is:
      12 - 12

    • Subtraction:
      12 - 12 = 0


100

4x+6=4x−2

Subtract 4x:
6=−2 ← False

Answer: No solution

100

The ratio of cats to dogs is 2:3. If there are 4 cats, how many dogs are there?

  • Set up proportion: 2/3 = 4/x

  • Cross multiply: 2 × x = 3 × 4

  • 2x = 12

  • Divide both sides by 2: x = 12 ÷ 2

  • x = 6

Answer:
There are 6 dogs.

100

3/4 + 2/5

  • Find common denominator: 20

  • Convert fractions: (3/4) = 15/20, (2/5) = 8/20

  • Add numerators: 15 + 8 = 23

  • Result: 23/20 = 1 3/20

Answer:
1 3/20

100

The test scores are:
4, 7, 9, 10, 6

Find the mean and median.

  • Mean (average):
    Add all numbers: 4 + 7 + 9 + 10 + 6 = 36
    Divide by the number of scores (5):
    Mean = 36 ÷ 5 = 7.2

  • Median (middle value):
    Sort the numbers: 4, 6, 7, 9, 10
    The middle number (3rd value) is: 7
    Median = 7

200

(3 + 2)^2 − 4 × 3


    • Parentheses first:
      3 + 2 = 5
      Now the expression is:
      5^2 - 4 * 3

    • Exponent:
      5^2 = 25
      Now the expression is:
      25 - 4 * 3

    • Multiplication:
      4 * 3 = 12
      Now the expression is:
      25 - 12

    • Subtraction:
      25 - 12 = 13


200

3(x - 1) = 9

  • Distribute: 3x - 3 = 9

  • Add 3: 3x = 12

  • Divide by 3: x = 4

Answer: x = 4

200

The ratio of apples to oranges is 3:2. If there are 9 apples, how many oranges are there?

Solution:

  • Set up the proportion: 3/2 = 9/x

  • Cross multiply: 3 × x = 2 × 9

  • 3x = 18

  • Divide both sides by 3: x = 18 ÷ 3

  • x = 6

200

7/9 + 2/6

  • Solution:

    • Find common denominator: 18

    • Convert: 7/9 = 14/18, 2/6 = 6/18

    • Add: 14 + 6 = 20

    • 20/18 = 1 2/18 → simplify: 1 1/9

  • Answer:
    1 1/9

200

2, 5, 11, 23, 47, ___, ___

(fun fact: this was a lot of my HSPT)

95, 191

300

5×(6+23)÷4


    • Parentheses:
      6+23=296+23=29
      Expression becomes:
      5×29÷45×29÷4

    • Multiplication:
      5×29=1455×29=145
      Expression becomes:
      145÷4145÷4

    • Division:
      145÷4=36.25145÷4=.   36.25


300

3(x−2)+4=19

Distribute: 3x−6+4=193x−6+4=19
Simplify: 3x−2=193x−2=19
Add 2: 3x=213x=21
Divide by 3:
x=7

Answer: x=7

300

If 4 pencils cost $6, how much do 10 pencils cost?

  • Set up the proportion: 4/6 = 10/x

  • Cross multiply: 4 × x = 6 × 10

  • 4x = 60

  • Divide both sides by 4: x = 60 ÷ 4

  • x = 15

Answer:
10 pencils cost $15.

300

2/7 + 3/11

LCD of 7 and 11 = 77
2/7 = 22/77
3/11 = 21/77
Add: 22 + 21 = 43
Result: 43/77 (already simplified)

Answer:
43/77

300

When was the last time Riordan Boys Basketball went to the open divisions state championships? When was the last time they won D1 CCS?

2025! and 2025!

400

[(2 + 3)^2 - 4] * 2 + 6


    • Parentheses inside brackets:
      2+3=52+3=5
      Now the expression is:
      [(5)^2 - 4] * 2 + 6

    • Exponent:
      52=2552=25
      Now:
      [25 - 4] * 2 + 6

    • Subtraction inside brackets:
      25−4=2125−4=21
      Now:
      21 * 2 + 6

    • Multiplication:
      21∗2=4221∗2=42
      Now:
      42 + 6

    • Addition:
      42+6=4842+6=48


400

3(x - 2) + 5 = 2x + 7

  • Distribute: 3x - 6 + 5 = 2x + 7

  • Simplify: 3x - 1 = 2x + 7

  • Subtract 2x: x - 1 = 7

  • Add 1: x = 8

Answer: x = 8

400

The ratio of apples to oranges is 1 to 2. There are 9 fruits total. How many apples and how many oranges are there?

Solution:

  • Add the parts of the ratio: 1 + 2 = 3 parts total.

  • Divide total fruits by total parts: 9 ÷ 3 = 3 fruits per part.

  • Apples = 1 part × 3 = 3 apples.

  • Oranges = 2 parts × 3 = 6 oranges.

400

7/4 + 2/3 − 5/6

  1. Find the least common denominator (LCD) of 4, 3, and 6:
    LCD = 12

  2. Convert all fractions to have a denominator of 12:
    7/4 = 21/12
    2/3 = 8/12
    5/6 = 10/12

  3. Perform the operations in order:
    21/12 + 8/12 = 29/12
    29/12 − 10/12 = 19/12

  4. Convert to mixed number:
    19 ÷ 12 = 1 remainder 7 → 1 7/12

400

What Was the ARHS girls flag football win streak?
a. 11

b. 15

c. 22

d. 19

22 games in a row 

500

6 + [2 × (3 + 4^2) - 5] ÷ 3


    • Exponent inside parentheses:
      42=1642=16
      Now the expression is:
      6 + [2 × (3 + 16) - 5] ÷ 3

    • Parentheses inside brackets:
      3+16=193+16=19
      Now:
      6 + [2 × 19 - 5] ÷ 3

    • Multiplication inside brackets:
      2×19=382×19=38
      Now:
      6 + [38 - 5] ÷ 3

    • Subtraction inside brackets:
      38−5=3338−5=33
      Now:
      6 + 33 ÷ 3

    • Division:
      33÷3=1133÷3=11
      Now:
      6 + 11

    • Addition:
      6+11=176+11=17


500

3(x - 1) + 4 = 3x + 2

  • Distribute: 3x - 3 + 4 = 3x + 2

  • Simplify: 3x + 1 = 3x + 2

  • Subtract 3x: 1 = 2 ← False statement

Answer: No solution

500

A recipe requires a ratio of 4 cups of milk to 7 cups of water. If you have 28 cups of water, how much milk do you need?

Solution:

  • Set up the proportion: 4/7 = x/28

  • Cross multiply: 7 × x = 4 × 28

  • 7x = 112

  • Divide both sides by 7: x = 112 ÷ 7

  • x = 16

Answer:
You need 16 cups of milk.

500

4/10 + 7/12 - 1/15

Solution:
LCD of 10, 12, and 15 = 60
4/10 = 24/60
7/12 = 35/60
1/15 = 4/60
Add/Subtract: 24 + 35 - 4 = 55
Result: 55/60 → simplified: 11/12

Answer:
11/12

500

The scores on a math quiz are:
8, 6, 9, 8, 7, 10, 8, 6

Find the mean, median, and mode of the scores.

  • Mean (average):
    Add all the scores and divide by the number of scores.
    Sum: 8 + 6 + 9 + 8 + 7 + 10 + 8 + 6 = 62
    Number of scores: 8
    Mean = 62 ÷ 8 = 7.75

  • Median (middle value when sorted):
    Sorted scores: 6, 6, 7, 8, 8, 8, 9, 10
    Since there are 8 scores (even number), median is average of 4th and 5th values.
    4th value: 8, 5th value: 8
    Median = (8 + 8) ÷ 2 = 8

  • Mode (most frequent):
    Look for the number that appears most often:
    8 appears 3 times
    Others appear fewer times
    Mode = 8

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