Equivalent Fractions
A fraction as a bar
A fraction describes part of a whole, and a bar makes it concrete: the bottom number says how many equal parts the whole is split into, and the top number says how many of those parts are taken. One half shades one of two parts; three quarters shades three of four. Seeing a fraction as a shaded bar gives it a definite size rather than leaving it as two numbers, and that size is the key to the whole unit, because equivalent fractions are exactly the ones that shade the same amount of the bar.
Equivalent fractions
Different fractions can describe the same amount: these are equivalent fractions. One half, two quarters and four eighths all shade exactly the same part of a bar, even though the numbers differ. They look different because the whole is cut into more or fewer pieces, but the shaded amount is identical. Recognising that the same value can be written many ways is the central idea of this unit. It explains why a half and two quarters are interchangeable, and it is the foundation for comparing, adding and simplifying fractions later on.
Making equivalents
Equivalent fractions are made by multiplying the top and bottom by the same number. Multiplying 1/2 top and bottom by 2 gives 2/4; by 3 gives 3/6. Because both parts are scaled together, the value does not change — only the number of pieces does. This gives related denominators: 2, 4, 6, 8 are all related to halves. Knowing how to build an equivalent with a chosen denominator is a practical skill, needed whenever fractions must be rewritten to share a common bottom number, and it follows directly from the meaning of equivalence.
Fractions and decimals
Fractions and decimals are two ways of writing the same kind of thing: a part of a whole. One half is 0.5, one quarter is 0.25, three quarters is 0.75. The link is clearest for tenths and hundredths, since 1/10 is 0.1 and 7/100 is 0.07, matching the decimal place-value columns met earlier. Connecting a fraction to its decimal form — and back — is written into this descriptor, because the two notations appear everywhere and a child needs to move between them freely, recognising that 1/2 and 0.5 are the same number.
Spotting equivalents
Telling whether two fractions are equivalent is the practical test of this unit. Two fractions are equivalent if one can be scaled to the other, or if both simplify to the same fraction: 2/4 and 1/2 are equivalent because 2/4 simplifies to 1/2. Checking equivalence — by scaling up or simplifying down — lets a child compare fractions and recognise the same value in disguise. This skill draws together the bar picture, the scaling rule and simplifying, and it is what makes equivalent fractions useful rather than just a definition.
Fractions, equivalents and decimals
Pulling the unit together, every fraction can be written as equivalent fractions and as a decimal. A table makes the connections plain: 1/2 equals 2/4 and 0.5; 3/4 equals 6/8 and 0.75. Equivalents come from scaling top and bottom together; the decimal comes from reading the fraction as tenths or hundredths. With fractions seen as bars, equivalence understood, equivalents built with related denominators, fractions linked to decimals, and equivalents spotted, a child can move freely between the different ways of writing a fractional amount — a skill at the centre of all later work with fractions.