Fractions, Decimals and Percentages – Full Parent Guide
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Fractions, Decimals and Percentages – Full Parent Guide
TL;DR
This guide explains fractions, decimals, and percentages as three representations of the same underlying quantity, showing how to convert between them fluently and where each form is most useful. You will see why the three forms are not separate topics but a single idea, and you will practise conversions with worked examples at every step.
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Bhanzu Team Last updated on May 11, 20268 min read
Fractions, decimals, and percentages are not three different topics — they are three different ways of writing the same thing.
That one sentence resolves most of the confusion children carry into secondary school. A child who has been taught fractions, decimals, and percentages as separate units — each with its own rules, its own symbols, its own chapter — will treat them as unrelated. A child who understands that 12\frac{1}{2}21, 0.50.50.5, and 5050%50 are identical in value will use whichever form a problem calls for without hesitation.
Understanding fractions decimals and percentages as a connected system — not three isolated topics — is the foundational shift that makes this cluster of mathematics learnable.
What is Actually Going on When Children Struggle
The most common source of difficulty with fractions, decimals, and percentages is not the arithmetic — it is a missing understanding of what a fraction is representing.
A fraction like 34\frac{3}{4}43 describes a relationship: 3 parts out of 4 equal parts of a whole. When children are taught fractions as a rule — "the top number divided by the bottom number" — they can compute but cannot reason.
They cannot estimate whether 34\frac{3}{4}43 is closer to 0 or 1. They cannot place it on a number line. They cannot see that 68\frac{6}{8}86 means the same thing.
The decimal and percentage confusions follow from the same root. 0.750.750.75 looks like a "small number" to a child who has not connected it to 34\frac{3}{4}43. 7575%75 feels abstract until the child understands it as "75 out of every 100 parts." None of this is hard to fix — but it requires going back to the meaning before the calculation.
Signs Your Child's Confusion is Conceptual, Not Procedural
Observable patterns that indicate the issue is deeper than needing more practice:
Your child can convert 12\frac{1}{2}21 to 0.50.50.5 but cannot place 0.50.50.5 on a number line between 0 and 1. They know the rule without understanding what the number represents.
Your child says 0.70.70.7 is smaller than 0.250.250.25 because "7 is smaller than 25." They are treating decimal digits as whole numbers — the decimal point has not anchored correctly.
Your child calculates 2020%20 of a number correctly using a method but cannot estimate whether 2020%20 is closer to a small or large portion of the original. The percentage has no intuitive meaning.
Your child treats 14+14=28\frac{1}{4} + \frac{1}{4} = \frac{2}{8}41+41=82 (adding numerators and denominators). This is the single most common fraction error — it shows the child has not understood that the denominator describes piece size, not a number to add.
The second-guesser is particularly visible here: they calculate 34+14\frac{3}{4} + \frac{1}{4}43+41, get 44\frac{4}{4}44, and then convert it to 11\frac{1}{1}11 — then doubt the answer and rewrite 48\frac{4}{8}84 because "44\frac{4}{4}44 doesn't look right." They got the right answer and then undid it because they lack confidence in what 44=1\frac{4}{4} = 144=1 means.
What To Do At Home To Teach Fractions Decimals and Percentages
These interventions are short and do not require teaching materials.
Use real objects to show equivalence. Cut an apple into 4 equal pieces. Ask how much one piece is (14\frac{1}{4}41). How much are two pieces (24\frac{2}{4}42 or 12\frac{1}{2}21)? How much as a percentage (5050%50)?
Same physical object, three ways of describing it. Repeat with a pizza, a chocolate bar, anything divisible into equal parts.
Display a reference strip, not flashcards. A laminated fraction-decimal-percentage reference strip (the common equivalents table above) displayed where your child does homework is more useful than testing them on conversions. The goal is fluency through repeated exposure, not memorisation through stress.
Ask "more than half or less than half?" Before any fraction, decimal, or percentage calculation, have your child estimate: is this value more than 12\frac{1}{2}21 (or 0.50.50.5, or 5050%50) or less? A child who can do this consistently has genuine number sense. A child who cannot has learned to calculate without understanding.
Connect percentages to shopping. "This item is 2020%20 off — roughly how much will we save?" Most children from age 9 upward can estimate 1010%10 of a price (move the decimal point one place). Double it for 2020%20. Half of 1010%10 for 55%5. Real-world estimation builds the intuition that formal calculation practice often misses.
Common Equivalents — The Values Every Child Should Know by Sight
| Fraction | Decimal | Percentage |
|---|---|---|
| 1100\frac{1}{100}1001 | 0.010.010.01 | 11%1 |
| 110\frac{1}{10}101 | 0.10.10.1 | 1010%10 |
| 15\frac{1}{5}51 | 0.20.20.2 | 2020%20 |
| 14\frac{1}{4}41 | 0.250.250.25 | 2525%25 |
| 13\frac{1}{3}31 | 0.333…0.333\ldots0.333… | 331333\frac{1}{3}%3331 |
| 12\frac{1}{2}21 | 0.50.50.5 | 5050%50 |
| 23\frac{2}{3}32 | 0.666…0.666\ldots0.666… | 662366\frac{2}{3}%6632 |
| 34\frac{3}{4}43 | 0.750.750.75 | 7575%75 |
| 45\frac{4}{5}54 | 0.80.80.8 | 8080%80 |
| 910\frac{9}{10}109 | 0.90.90.9 | 9090%90 |
| 111 | 1.01.01.0 | 100100%100 |
| 54\frac{5}{4}45 | 1.251.251.25 | 125125%125 |
| 32\frac{3}{2}23 | 1.51.51.5 | 150150%150 |
Display this table somewhere your child can see it — familiarity with these values by sight is worth more than any conversion drill.
How To Convert Between Fractions, Decimals And Percentages — Worked Examples
There are six conversion directions. Each is a single rule with a worked step.
1. Fraction → Decimal
Rule: Divide the numerator (top) by the denominator (bottom).
Example: Convert 38\dfrac{3}{8}83 to a decimal.
3÷8=0.3753 \div 8 = 0.3753÷8=0.375
Answer: 38=0.375\dfrac{3}{8} = 0.37583=0.375
2. Decimal → Fraction
Rule: Write the decimal over 1, multiply top and bottom by 10 for each decimal place, then simplify.
Example: Convert 0.750.750.75 to a fraction.
0.751→×10075100→simplify34\frac{0.75}{1} \xrightarrow{\times 100} \frac{75}{100} \xrightarrow{\text{simplify}} \frac{3}{4}10.75×10010075simplify43
Answer: 0.75=340.75 = \dfrac{3}{4}0.75=43
3. Percentage → Decimal
Rule: Divide the percentage by 100 (equivalently, move the decimal point 2 places left) and remove the % sign.
Example: Convert 3535%35 to a decimal.
3535% \div 100 = 0.3535
Answer: 3535% = 0.3535
4. Decimal → Percentage
Rule: Multiply by 100 (move the decimal point 2 places right) and add the % sign.
Example: Convert 0.60.60.6 to a percentage.
0.6×100=600.6 \times 100 = 600.6×100=60
Answer: 0.6=600.6 = 60%0.6=60
5. Fraction → Percentage
Rule: Divide the numerator by the denominator, then multiply by 100%.
Example: Convert 720\dfrac{7}{20}207 to a percentage.
7÷20=0.35→×100357 \div 20 = 0.35 \xrightarrow{\times 100} 35%7÷20=0.35×10035
Answer: 720=35\dfrac{7}{20} = 35%207=35
6. Percentage → Fraction
Rule: Write the percentage as a fraction over 100, then simplify.
Example: Convert 8080%80 to a fraction.
8080% = \frac{80}{100} \xrightarrow{\text{simplify}} \frac{4}{5}80
Answer: 8080% = \dfrac{4}{5}80
Quick Reference: Which Operation To Use
| Converting from → to | Operation |
|---|---|
| Fraction → Decimal | Divide numerator ÷ denominator |
| Decimal → Fraction | Write over 1, × by 10^(decimal places), simplify |
| % → Decimal | ÷ 100 (move decimal 2 left) |
| Decimal → % | × 100 (move decimal 2 right) |
| Fraction → % | Divide top ÷ bottom, then × 100 |
| % → Fraction | Write over 100, simplify |
When To Get Outside Help
Two signals are worth acting on rather than waiting.
If your child is in Year 6 or Grade 6 and cannot place 34\frac{3}{4}43, 0.750.750.75, and 7575%75 on a number line, the conceptual gap is significant enough to affect secondary school mathematics from the first week. A short period of structured intervention — a tutor or a structured programme — before secondary transition is highly effective at this point.
If your child can perform fraction calculations in class but cannot apply them in unfamiliar problems (for example, they know how to add fractions but cannot figure out what fraction of a class of 28 students is 7 students), the conceptual understanding has not formed. More practice on the same type of problem will not close this gap; a different explanation approach will.
How This Programme Approaches Fractions, Decimals and Percentages
This programme introduces fractions through the language of parts and wholes — concrete, visual, physical — before any rule or symbol appears. A student who understands that 34\frac{3}{4}43 means three out of four equal parts of something real will find the decimal and percentage representations natural extensions rather than new subjects.
The three-representation approach is applied consistently: every fraction concept is shown as a fraction, a decimal, and a percentage simultaneously, so the child builds the equivalence understanding from the beginning rather than learning to convert later.
This programme fits families where the child is in Grades 4–9 and the confusion with fractions, decimals, or percentages is affecting their broader math confidence. The programme does not replace a specialist intervention for children with identified learning differences affecting number sense.
How Fractions Decimals and Percentages Connect Across Year Groups
In Grades 3–4 (Years 3–4), children first encounter fractions as parts of a shape or group. This stage is entirely visual and concrete — no decimals or percentages yet. The conceptual anchor is the equal-parts definition: a fraction only makes sense when the whole is divided into pieces of the same size.
In Grades 5–6 (Years 5–6), decimals are introduced as an extension of the place-value system, and percentages are introduced as fractions with a denominator of 100. At this stage, children who understand fractions as parts of a whole find the extensions natural. Children who memorised fraction rules find each new form confusing.
By Grades 7–8 (Years 7–8), all three forms are used interchangeably in problems involving ratio, proportion, and probability. A student who can move fluently between 35\frac{3}{5}53, 0.60.60.6, and 6060%60 has a significant advantage in every topic that follows. A student who treats them as three separate subjects must look up conversions mid-problem — which compounds calculation errors and reduces confidence.
The school-by-school sequencing varies, but the conceptual path is consistent internationally — confirmed across multiple international curricula including Common Core (US), the UK National Curriculum, the Australian Curriculum, and CBSE (India).
Frequently Asked Questions
Why do fractions decimals and percentages confuse children so much?
Fractions Decimals and Percentages are usually taught as three separate topics in three different school terms, often with different teachers, different textbooks, and different symbols. The connection between them — that they all express parts of a whole — is rarely made explicit at the time of introduction. Children who are taught the connection first, and the notation second, find all three significantly more accessible.
What percentage and decimal conversions should my child know by heart?
The most useful ones are: 12=0.5=50\frac{1}{2} = 0.5 = 50%; 14=0.25=25\frac{1}{4} = 0.25 = 25%; 34=0.75=75\frac{3}{4} = 0.75 = 75%; 15=0.2=20\frac{1}{5} = 0.2 = 20%; 110=0.1=10\frac{1}{10} = 0.1 = 10%. Knowing these by sight removes a large number of calculation steps from standardised problems.
My child adds fractions by adding the numerators and denominators separately. How do I fix this?
Go back to the physical model. Cut a piece of paper into four equal pieces. Take one piece, then another — how many pieces out of four?
Two. So the answer is 24\frac{2}{4}42.
At what age should children understand percentages?
Most curricula introduce percentages in Year 5 or Grade 5 (ages 9–10), building on fraction understanding from Years 3–4. However, informal percentage exposure — "20% off," "half price," "three-quarters full" — is useful from age 6 onward. Connecting percentage to everyday contexts before formal instruction is introduced makes the formal learning significantly easier.