Convert between fractions, decimals, and percents. |...

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.

Fraction

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

Decimal

Tenths, hundredths after the point. Great for adding.

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

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 = \frac{Numerator}{Denominator}

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

DECIMAL → PERCENT

Percent = Decimal × 100

Example: 0.75 × 100 = 75%

PERCENT → FRACTION

\frac{Percent}{100}

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

SECTION 5

Detailed Breakdown

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!

Quick Reference Table

Fraction	Decimal	Percent
1/10	0.1	10%
3/5	0.6	60%

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

Step 1: Fraction to DecimalDivide 5 by 8: 5 ÷ 8 = 0.625

0.625

Step 2: Decimal to PercentMultiply 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

Form	Strengths	Limitations
Fraction	Exact for sharing; shows parts clearly.	Hard to add unlike ones.
Decimal	Easy to add and compare.	Repeating ones like 1/3 = 0.333...
Percent	Quick 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.

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

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

SECTION 9

Practice Problems

PROBLEM 1 — CONCEPTUAL

Which shows the same amount as 1/2? A. 0.2 B. 0.5 C. 25% D. 1/4 E. 0.02

PROBLEM 2 — BASIC CALCULATION

Convert 3/10 to a decimal. A. 0.3 B. 0.03 C. 30% D. 3/100 E. 0.13

PROBLEM 3 — INTERMEDIATE

What percent is 7/20? A. 35% B. 3.5% C. 20% D. 70% E. 14%

PROBLEM 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

PROBLEM 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%

SUMMARY

Lesson 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!