Faster for
Decimals
Adding, subtracting, and comparing sizes. Line up the dot and the answer is visible immediately.
SSAT Upper Level Prep Masterclass · Topic 4
Fractions & Decimals
You have used these for years. The Upper Level tests whether you can use them fast, accurately, and in either direction.
Lesson summary
Welcome to the Math section of your SSAT Upper Level course! While you have used fractions and decimals for years, the Upper Level exam requires you to use them with speed, accuracy, and flexibility. Today, we will master the art of converting between formats, handling arithmetic with mixed numbers, and navigating the most common trap answers on the SSAT. By the end of this lesson, you will be prepared to solve any rational number problem the exam throws your way.
Direct instruction
Welcome to Upper Level math
On the SSAT Upper Level exam, the Quantitative sections are designed to challenge your speed and logic. You will face 50 math questions, and a significant portion of them will test your ability to manipulate fractions and decimals.
At this level, you won’t just be asked what $\frac{1}{2} + \frac{1}{4}$ is. You will be asked to compare mixed numbers, solve multi-step problems involving decimals, and recognize relationships between percentages and fractions.
Strategy 1: convert to improper fractions
When you encounter mixed numbers like $2\frac{1}{3}$ in a problem, they are difficult to manage. The best strategy for the Upper Level exam is to convert every mixed number into an improper fraction immediately.
-
Multiply the whole number by the denominator
$2 \times 3 = 6$
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Add the numerator
$6 + 1 = 7$
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Place that over the original denominator
The result is $\frac{7}{3}$.
$$2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$$
Improper fractions are much easier to multiply, divide, and simplify than mixed numbers.
Strategy 2: decimal discipline, line up the dot
When working with decimals, the number one source of careless errors is place-value misalignment.
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The rule
If you are adding or subtracting decimals, rewrite them vertically on your scratch paper.
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The check
Draw a straight line down through all the decimal points. If they are not in a perfectly straight column, your math will be wrong.
-
The placeholder
Always fill empty spaces with a zero, so $4.5 – 1.25$ gets written as $4.50 – 1.25$.
Strategy 3: pick one language
The SSAT Upper Level often mixes formats, for example asking you to solve:
$$0.8 + \frac{1}{5}$$
You cannot operate on numbers that speak different languages. Choose one format, either fractions or decimals, and convert both numbers into it.
Faster for
Better for
Fractions
Multiplication and division, especially when values cancel and leave you clean numbers.
SSAT tip: benchmark conversions
Memorizing the most common conversions gives you a major speed advantage. If you know these on sight, you save 30 to 60 seconds per problem:
| Fraction | Decimal | Percent |
|---|---|---|
| $\frac{1}{2}$ | $0.5$ | 50% |
| $\frac{1}{4}$ | $0.25$ | 25% |
| $\frac{3}{4}$ | $0.75$ | 75% |
| $\frac{1}{5}$ | $0.2$ | 20% |
| $\frac{1}{8}$ | $0.125$ | 12.5% |
Worked examples
1
Worked example
Adding two mixed numbers
Scenario
Solve: $1\frac{1}{4} + 2\frac{2}{3}$
Step by step
- First, convert both mixed numbers into improper fractions: $1\frac{1}{4} = \frac{5}{4}$ and $2\frac{2}{3} = \frac{8}{3}$.
- Now we need a common denominator for $4$ and $3$, which is $12$.
- Convert $\frac{5}{4}$ into $\frac{15}{12}$ by multiplying the top and bottom by $3$.
- Convert $\frac{8}{3}$ into $\frac{32}{12}$ by multiplying the top and bottom by $4$.
- Add the numerators: $15 + 32 = 47$.
$$\frac{15}{12} + \frac{32}{12} = \frac{47}{12} = 3\frac{11}{12}$$
Takeaway
The answer is $\frac{47}{12}$, which is $3\frac{11}{12}$.
Why this is correct
Converting to improper fractions avoids the common mistake of adding whole numbers and fractions separately, which leads to errors when you have to regroup at the end.
2
Worked example
Subtracting from a whole number
Scenario
Solve: $15 – 4.67$
Step by step
- Marcus writes the problem vertically, because he knows he must line up the decimal points.
- He rewrites $15$ as $15.00$ so both numbers have the same number of decimal places.
- He borrows across the decimal point and subtracts column by column.
$$\begin{array}{r} 15.00 \\ -\;4.67 \\ \hline 10.33 \end{array}$$
Takeaway
The answer is $10.33$.
Why this is correct
Writing $15.00$ keeps Marcus out of two classic traps: treating $0 – 7$ as $7$, and subtracting the whole numbers first ($15 – 4 = 11$) before handling the decimals, which lands you on $11.33$ instead of $10.33$.
3
Worked example
Comparing across formats
Scenario
Which is larger: $\frac{5}{8}$ or $0.6$?
Step by step
- Chloe needs to compare these two numbers, but they are in different formats.
- She decides to convert $\frac{5}{8}$ into a decimal.
- She knows the benchmark $\frac{1}{8} = 0.125$.
- Therefore $\frac{5}{8} = 0.125 \times 5 = 0.625$.
- Now she compares $0.625$ with $0.6$, which is the same as $0.600$.
Takeaway
$\frac{5}{8}$ is larger than $0.6$.
Why this is correct
By converting the fraction to a decimal and padding with placeholder zeros so both have the same length, the comparison between $0.625$ and $0.600$ becomes immediate.
Short review
Key points covered
- Improper fractions: use these instead of mixed numbers when doing arithmetic.
- Decimal alignment: line up the decimal point vertically and use placeholder zeros to avoid subtraction errors.
- Conversion: always match your formats, all decimals or all fractions, before performing any operation.
Important reminders
- The SSAT loves to test your ability to convert. If you see a mix of formats, convert to decimals for comparison, or to fractions for multiplication.
- Always simplify your final fraction, or the answer key may not appear to contain your result.
Study tips
- Spend 5 minutes today drilling the benchmark conversions in the table above. These are the sight words of SSAT math, and knowing them instantly saves you a large amount of time.
You are making excellent progress!
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