From one bag of flour, 3/8 goes into bread and 2/5 goes into pancakes. What fraction of the bag is used altogether?
Hint: Can you write both fractions with the same bottom number first?
Answer: 31/40
Year 6 Fractions Worksheets with Answers (PDF)
Imaginesis: printable Year 6 Fractions maths worksheets for England (National Curriculum) — Add and subtract fractions with different denominators, Multiplying Decimals by Whole Numbers, Dividing Unit Fractions and Whole Numbers: word problems with hints, answers and worked solutions as PDF, also as an A/B test.
Sample word problems
Sam sits by the vegetable patch to measure garden wire for supporting his squash plants. He cuts 4 pieces of wire from a spool, with each piece measuring 2.2 metres long. How many metres of wire did Sam cut altogether?
Hint: To find the total length of wire for the squash plants, think about combining 4 equal groups that each measure 2.2 metres. Decide whether to add that same length 4 times or use multiplication to find the combined length in metres.
Answer: 8.8
A road crew has 8 tonnes of asphalt for patching potholes, and every pothole takes 1/7 of a tonne. How many potholes can the crew fill?
Hint: Work out how many portions of 1/7 fit into one tonne, then into all of them.
Answer: 56
Objectives in this topic
Add and subtract fractions with different denominators
Children learn to add and subtract fractions with different denominators by rewriting them as equivalent fractions with a shared denominator.
Y5.F.4 add and subtract fractions with the same denominator and denominators that are multiples of the same numberY6.F.3 add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions
In Year 6, children calculate with fractions that have different denominators. Building on previous experience with denominators that were direct multiples of one another, they use equivalent fractions to rewrite both parts of an addition or subtraction problem so that they share a common denominator before completing the calculation.
A common error occurs when children add or subtract straight across, combining the numerators and the denominators directly (such as writing 1/3 + 1/4 = 2/7). This usually happens when pupils treat fractions as two separate whole numbers rather than remembering that fractions of different sizes cannot be combined until they are converted into equal parts.
Worksheet tasks provide targeted practice across these operations. Children solve direct calculation questions using Add fractions with unlike denominators and Subtract fractions with unlike denominators, or tackle contextual problems in How much altogether? Unlike fractions to find combined totals.
Multiplying Decimals by Whole Numbers
Children learn to multiply one-digit numbers with up to two decimal places by whole numbers, applying written methods to arithmetic and measurement questions.
KS3.N.4 use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negativeY6.F.8 multiply one-digit numbers with up to two decimal places by whole numbers
In Year 6, children learn to multiply numbers with up to two decimal places by a whole number, such as calculating 3.45 × 6 or 8.2 × 4. They use standard written methods for multiplication, drawing on their understanding of place value to know how tenths and hundredths scale when multiplied.
A common error occurs when placing the decimal point in the final answer. Children frequently carry out the multiplication accurately as if working with whole numbers, but then misplace or omit the decimal point at the end, resulting in an answer that is ten or a hundred times too large (for example, writing 1380 instead of 13.8).
Worksheets for this skill feature two typical styles of tasks:
- Multiply decimals provides direct written calculations to solve, reinforcing fluency and accurate decimal placement.
- Multiply a length by a number of pieces sets the calculation within real-world measurement problems, such as finding the total length of six pieces of ribbon measuring 1.45 metres each.
Dividing Unit Fractions and Whole Numbers
Children learn to divide unit fractions by whole numbers and calculate how many unit fractions fit into a given whole number.
Y6.F.5 divide proper fractions by whole numbers [for example, 1/3 ÷ 2 = 1/6]
In Year 6, children learn to divide proper fractions by whole numbers, such as calculating 1/3 ÷ 2 = 1/6, and explore how whole numbers divide by unit fractions. They learn that splitting a fraction into equal parts results in smaller fraction pieces, doubling the denominator when dividing by two.
A frequent mistake happens when children confuse the operation and multiply the numerator instead of the denominator, writing 1/3 ÷ 2 = 2/3. Because division with whole numbers usually produces a smaller answer, children can also become confused when dividing a whole number by a fraction results in a larger number.
Practice tasks such as How many unit fractions fit? help resolve this by asking children to find how many unit fractions (like 1/3 or 1/4) fit inside a given whole number. This builds a clear mental picture of division as grouping before moving on to purely numerical calculations.