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SSAT Middle Level: Quantitative • Fractions, Decimals, and Percents

Convert between fractions, decimals, and percents.

Unlock the power to switch between these three ways to show parts of a whole.

Explore the lesson 4 min read
SSAT Middle Level illustration with a test notebook, quantitative function, and reading book
Inside this lesson 10 sections 5 questions 8 figures

SECTION 1

Historical Context & Motivation

Long ago, people needed ways to share things like food or land fairly. Fractions started with ancient Egyptians around 1800 BCE. They used them to divide loaves of bread. Decimals came later in the 1500s from a smart mathematician named Simon Stevin. Percents mean 'per hundred' and grew popular in the 1400s for money and taxes. These tools solve the same problem: showing parts of a whole. You will use them a lot on the SSAT!

1800 BCE • Fractions Begin

Egyptians use unit fractions like 1/3 for dividing resources.

1585 • Decimals Invented

Simon Stevin publishes decimals for easy calculations in trade.

1400s • Percents Spread

Italian merchants use percents for interest and profits.

Today • SSAT Prep

You convert them quickly to ace Quantitative questions!

These inventions make math easier for everyday life, like scoring in games or sharing pizza. On the SSAT, you convert between them to solve problems fast. Get ready to master this skill!

SECTION 2

Core Principles & Definitions

A fraction shows part over whole, like 1/2 means one out of two equal parts. A decimal uses base-10 place values after a point, like 0.5. A percent is parts per hundred, like 50% with the % sign. All three say the same amount in different ways.

1

Fraction

Numerator (top) over denominator (bottom). Simplifies sharing.
2

Decimal

Tenths, hundredths after the point. Great for adding.
3

Percent

Times 100 with %. Perfect for discounts or scores.
✦

KEY TAKEAWAY

Think of them like pizza: 1/2 slice, 0.5 of the pie, or 50% full. Same tasty amount, different labels!

SECTION 3

Visual Explanation

Converting Between Fractions, Decimals & Percents Visualizing equivalent representations of the same value 1 2 3 5 slices unshaded ⅜ Fraction 3/8 = . Decimal 0.375 = % Percent 37.5% 3 ÷ 8 × 100 3 out of 8 equal slices are shaded Each slice = 1/8 = 12.5% Shaded (3/8) Unshaded (5/8)
This pie chart shows 3/8 shaded blue-to-pink. Arrows point to its decimal 0.375 and percent 37.5%. See how they match?

Look at the diagram above. The shaded part is the same no matter if you call it a fraction, decimal, or percent. This visual helps you see they are equal. You can draw quick sketches like this on test day!

SECTION 4

Mathematical Framework

To convert, use simple rules. Start with fraction to decimal: divide numerator by denominator. For decimal to fraction, read the places. Percent is easy: divide by 100.

FRACTION → DECIMAL

Decimal=NumeratorDenominatorDecimal = \frac{Numerator}{Denominator}

Example: 34=0.75\frac{3}{4} = 0.75

DECIMAL → PERCENT

Percent=Decimal×100Percent = Decimal × 100

Example: 0.75 × 100 = 75%

PERCENT → FRACTION

Percent100\frac{Percent}{100}

Example: 25% = 25100=14\frac{25}{100} = \frac{1}{4}

SECTION 5

Detailed Breakdown

Fractions, Decimals & Percents on a Number Line Every point can be expressed three ways 0 1 FRACTION 1/4 DECIMAL 0.25 25% FRACTION 1/2 DECIMAL 0.50 50% FRACTION 3/4 DECIMAL 0.75 75% Each point shows three equivalent representations of the same value
Number line from 0 to 1 marks common values. Pink at 1/4, blue at 1/2, orange at 3/4. Each shows fraction, decimal, and percent together.

The number line diagram lines up the three forms perfectly. Notice how 0.25 sits right under 1/4 and 25%. Use this to check your work. Practice spotting these matches!

FractionDecimalPercent
1/100.110%
3/50.660%

Quick Reference Table

SECTION 6

Worked Example

Suppose you have 5/8 of a game level complete. Convert it to decimal and percent. Follow these steps carefully.

Convert 5/8

  1. 1

    Step 1: Fraction to Decimal

    Divide 5 by 8: 5 ÷ 8 = 0.625
    0.625
  2. 2

    Step 2: Decimal to Percent

    Multiply by 100: 0.625 × 100 = 62.5Add % sign.
    62.5%

Great job! You just converted step by step. This method works every time on the SSAT.

SECTION 7

Strengths & Limitations

FormStrengthsLimitations
FractionExact for sharing; shows parts clearly.Hard to add unlike ones.
DecimalEasy to add and compare.Repeating ones like 1/3 = 0.333...
PercentQuick for real life like sales.Always out of 100; less flexible.
★

Key takeaway

Pick the best form like choosing a video game controller: fractions for dividing teams, decimals for scores, percents for win rates.

SECTION 8

Connection to Advanced Topics

These basics lead to ratios and proportions in harder math. On SSAT, you might solve 'What percent is 3/5?' which is 60%. Later, in algebra, they help with equations like rates.

BasicAdvanced
Convert 1/4 = 25%Solve 20% of x = 15 (x=75)
0.6 to fraction 3/5Percent change: (new-old)/old ×100%

Mastering conversions now builds confidence for tougher SSAT questions. You are on your way!

SECTION 9

Practice Problems

Question 1: CONCEPTUAL

Which shows the same amount as 1/2? A. 0.2 B. 0.5 C. 25% D. 1/4 E. 0.02
Show answer
B is correct: 1/2 = 0.5. A is 1/5 (too small). C is 1/4. D is half of 1/2. E is 1/50 (way too small). Remember halves are 0.5 or 50%!

Question 2: BASIC CALCULATION

Convert 3/10 to a decimal. A. 0.3 B. 0.03 C. 30% D. 3/100 E. 0.13
Show answer
A is correct: 3 ÷ 10 = 0.3. B moves decimal wrong. C is percent (30%). D is smaller fraction. E is random. Divide top by bottom!

Question 3: INTERMEDIATE

What percent is 7/20? A. 35% B. 3.5% C. 20% D. 70% E. 14%
Show answer
A is correct: (7 ÷ 20) = 0.35 × 100 = 35%. B forgets ×100 fully. C is denominator. D doubles numerator wrong. E halves it. Show steps: divide then ×100.

Question 4: APPLIED

Sara scored 4/5 on a test. What decimal is that? A. 0.8 B. 80% C. 0.4 D. 0.45 E. 4.5
Show answer
A is correct: 4 ÷ 5 = 0.8. B is percent form. C is 2/5. D averages wrong. E misplaced decimal. In school scores, fractions to decimals help compare grades!

Question 5: CRITICAL THINKING

Convert 0.24 to a fraction in simplest terms, then percent. A. 6/25, 24% B. 24/100, 0.24% C. 12/50, 24% D. 3/12.5, 24% E. 24/1000, 2.4%
Show answer
A is correct: 0.24 = 24/100 = 6/25, and 24%. B not simplified. C equals but not simplest. D wrong denominator. E too small. Simplify by dividing num/den by 4!

SUMMARY

Lesson Summary

Summary

You can now convert between fractions, decimals, and percents. Divide for decimals, ×100 for percents, /100 for fractions back. Visuals like pies and lines make it stick.

Practice these on SSAT to build speed and confidence. You got this—keep converting and conquering!

Varsity Tutors • SSAT Middle Level • Convert between fractions, decimals, and percents.