04
ISEE Middle Prep Masterclass · Topic 4

Fractions & Decimals

Fractions and decimals are two languages saying the same thing. Learn to translate and these questions become easy.

Both math sections
Benchmark conversions
Decimal traps

Lesson summary

Welcome back, test strategists! In this math lesson, we are going to tackle two topics that show up everywhere on the ISEE Middle Level exam: fractions and decimals. You will learn the golden rule of translating, discover how to easily compare messy numbers, and learn the secret shortcuts that dodge the most common traps the test-makers set. Let’s decode the math!

Direct instruction

Welcome to the translation zone

As you prepare for the ISEE, you will notice that the test-makers love to mix things up. They might give you a word problem containing both fractions and decimals, or ask you to compare two numbers that look completely different. To beat these questions, think of yourself as a math translator.

Fractions and decimals are just two different languages saying the exact same thing. “One half,” $\frac{1}{2}$, and $0.5$ all represent exactly the same amount of pizza! Once you can translate between the two, these questions become a breeze.

Where will you see this on the ISEE?

Fractions and decimals appear in both math sections, but they are tested in different ways:


Section 2

Quantitative Reasoning

Quantitative comparisons, where you decide whether Column A, often a fraction, is bigger than Column B, often a decimal.


Section 4

Mathematics Achievement

Standard word problems that require you to add, subtract, multiply, or divide these numbers.

The golden rule of translating

When a question gives you a mix of fractions and decimals, never do the math while they are in different languages.

Before you add, subtract, or compare, translate them so they match. Turn everything into fractions, or turn everything into decimals. Pick whichever language is easier for that particular problem.

Three habits that save you time

  • Memorize your benchmarks

    You should know the most common conversions instantly, without stopping to work them out. The table below is worth copying into your notebook.

  • Line up the dots

    When adding or subtracting decimals, line up the decimal points perfectly on your scratch paper first. Add invisible zeroes to the end of a number if you need the lengths to match.

  • Count the jumps

    When multiplying decimals, ignore the dots at first. Multiply like normal numbers, then count how many decimal jumps were in the original problem and put them back into your answer.

Fraction Decimal Say it out loud
$\frac{1}{2}$ $0.5$ One half
$\frac{1}{4}$ $0.25$ One quarter
$\frac{3}{4}$ $0.75$ Three quarters
$\frac{1}{5}$ $0.2$ One fifth
$\frac{2}{5}$ $0.4$ Two fifths
$\frac{1}{10}$ $0.1$ One tenth

Worked examples

1
Worked example

The carpenter’s board

Question

A carpenter has a wooden board that is $8.5$ feet long. He cuts off a piece that is $2\frac{1}{4}$ feet long. How long is the board now?

  • $6\frac{1}{4}$ feet
  • $6.25$ feet
  • $10.75$ feet
  • Both A and B

Step by step

  1. Spot the mix. We have a decimal, $8.5$, and a fraction, $2\frac{1}{4}$.
  2. Apply the golden rule. Translate them into the same language. Decimals are usually faster to subtract.
  3. Translate. From your benchmarks, $\frac{1}{4} = 0.25$, so $2\frac{1}{4}$ becomes $2.25$.
  4. Do the math. Line up the decimals and add a placeholder zero so both numbers are the same length.
$$\begin{array}{r} 8.50 \\ -\;2.25 \\ \hline 6.25 \end{array}$$
  1. Check the answers. The result is $6.25$ feet. But look at choice A: $6\frac{1}{4}$ is the exact same number.
Takeaway

The answer is D, both A and B.

Why this is correct

Translating the fraction into a decimal, lining up the points, and adding the placeholder zero solved the subtraction cleanly. Then reading every choice caught the fact that two of them were the same value written two ways.

2
Worked example

A quantitative comparison

Question

Compare the two columns.   Column A: $\frac{3}{8}$   Column B: $0.4$

  • Column A is greater.
  • Column B is greater.
  • The columns are equal.
  • There is not enough information to decide.

Step by step

  1. Apply the golden rule. Compare them in the same language. Let’s turn Column B into a fraction.
  2. Translate. $0.4$ is four tenths, written $\frac{4}{10}$. Dividing top and bottom by 2 gives $\frac{2}{5}$.
  3. Cross-multiply. Multiply diagonally, bottom to top. The $8$ under A times the $2$ on top of B gives $16$, which belongs to Column B. The $5$ under B times the $3$ on top of A gives $15$, which belongs to Column A.
  4. Compare. $16$ is bigger than $15$, so Column B is larger.
$$\frac{3}{8} \quad\text{vs}\quad \frac{2}{5} \qquad\Rightarrow\qquad 15 \;\;\text{vs}\;\; 16$$
Takeaway

The answer is B, Column B is greater.

Why this is correct

Turning the decimal into a fraction and cross-multiplying avoids long decimal division on your scratch paper. It is a brilliant shortcut for quantitative comparisons.

3
Worked example

The decimal multiplication trap

Question

What is the value of $1.2 \times 0.03$?

  • $3.6$
  • $0.36$
  • $0.036$
  • $0.0036$

Step by step

  1. Ignore the decimals first. Pretend the dots don’t exist, so the problem becomes $12 \times 3$.
  2. Do the simple math. $12 \times 3 = 36$.
  3. Count the jumps. In $1.2$ there is 1 digit behind the dot. In $0.03$ there are 2 digits behind the dot. That is $1 + 2 = 3$ jumps in total.
  4. Put the jumps back. Start from $36$ and move the decimal point three places to the left, filling the empty place with a zero.
$$36 \;\to\; 3.6 \;\to\; 0.36 \;\to\; 0.036$$
Takeaway

The answer is C, $0.036$.

Why this is correct

Test-makers deliberately put $3.6$ and $0.36$ in the options to catch students who guess at the decimal point. Ignoring the dots, doing the easy math, and carefully counting the jumps bypasses the trap entirely.

Short review

Key points covered

  • The golden rule: never mix fractions and decimals in the same calculation. Translate them into one language first.
  • Comparing fractions: cross-multiply. Multiply the bottom of one fraction by the top of the other to see which side is heavier.
  • Multiplying decimals: ignore the dots, multiply the plain numbers, then count the total decimal places to put back.

Important reminders

  • Read every answer choice before you commit. The ISEE sometimes writes the same value two different ways.
  • When you subtract decimals, add placeholder zeroes so both numbers have the same length.

Study tips

  • Copy the benchmark table into your ISEE notebook. Knowing that $\frac{1}{4} = 0.25$ and $\frac{1}{5} = 0.2$ on sight will save you a large amount of time on test day.

You are well on your way to becoming a master translator.

Grab your scratch paper, give your brain a quick stretch, and click the Mark Complete button below to put your new skills to the test!

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