Today we'll explore how fractions represent parts of a whole and why they are useful in everyday life. First, remember that a fraction is a part of a whole—think of sharing a mango among friends. Our learning goals are to identify equivalent fractions, compare them, add and subtract them, and work with mixed numbers and improper fractions. We'll connect these ideas to familiar Kenyan contexts, like dividing water bottles or portions of ugali. If anyone has questions as we go, just raise your hand and we'll pause to check understanding.
Notice this point: the same part of a whole, even if the pieces look different. That's the core idea – 1/2, 2/4, and 3/6 all cover the same amount of the whole. At this simple table. It shows that 1/2 equals 2/4, which also equals 3/6. Each column represents the same size slice of a whole, just divided into more pieces. Let's bring this home with a Kenyan example. If we cut a chapati into 2 pieces, each piece is 1/2 of the chapati. Cut the same chapati into 4 pieces and take 2 pieces – that's 2/4, which is still half of the chapati. Cut it into 6 pieces and take 3 – that's 3/6, also half. Whenever you see fractions that look different, check if they represent the same portion of the whole. That's what we call equivalent fractions (sehemu sawa).
Class, today we'll explore two handy ways to compare fractions that have different denominators. First, the Common Denominator method: we find a number that both denominators can divide into, then rewrite each fraction with that shared denominator. For example, to compare 1⁄4 and 2⁄5, the common denominator is 20. We convert 1⁄4 to 5⁄20 and 2⁄5 to 8⁄20; now we can see that 8⁄20 is larger. The second strategy is Cross‑Multiplication, which is quicker for Grade 5. We multiply across the fractions and compare the two products. Using the same fractions, 1⁄4 ? 2⁄5 becomes 1×5 = 5 and 2×4 = 8; because 8 is greater than 5, 2⁄5 is the larger fraction. Let's apply what we've learned to a Kenyan context. Imagine we have two families sharing maize meal. Family A gets 3⁄8 of a bag, while Family B gets 2⁄5. Using cross‑multiplication: 3×5 = 15 and 2×8 = 16, so 2⁄5 (Family B) receives the larger share. Remember: the common denominator gives a visual rewrite, while cross‑multiplication lets you compare quickly. Use whichever feels more comfortable in the moment.
Welcome, everyone! First, look at these key ideas: when the denominators are the same, we simply add or subtract the numerators; when they are different, we must find a common denominator before we combine them. Here we have one‑fourth plus one‑sixth. To add them, we need a common denominator – the least common multiple of 4 and 6 is 12. We rewrite the fractions: 1/4 becomes 3/12 and 1/6 becomes 2/12. We can add the numerators: 3 + 2 equals 5, so the sum is 5/12. In the Kenyan context, imagine a water tank that is 1/4 full and another tank that is 1/6 full. Together they hold 5/12 of a full tank – a useful way to plan how much water we have. Remember: like denominators → add or subtract numerators directly; unlike denominators → find a common denominator first. Any questions before we move on?
Class, today we're going to explore mixed numbers and improper fractions, and see how to move between them. First, a mixed number is simply a whole number plus a fraction. For example, 2 ⅓ means 2 whole units and one third of another unit. Second, an improper fraction is a fraction where the numerator is larger than the denominator, like 7⁄3. Let's convert 2 ⅓ to an improper fraction. We multiply the whole number 2 by the denominator 3, add the numerator 1, and place that over 3. 2 ⅓ = (2×3+1)/3 = 7⁄3.
